Solve using the quadratic formula:?

x² - 3x - 3 = 5
x² - 3/2x = 8 + (- 3/2)²
x² - 3/2x = 32/4 + 9/4
(x - 3/2)² = 41/4
x - 3/2 = 3.2015621

x = 3.2015621 + 1.5, x = 4.7015621
x = - 3.2015621 + 1.5, x = - 1.7015621

Answer: x = 4.7015621, - 1.7015621. Proofs are given below:

Proof:
4.7015621² - 3(4.7015621) - 3 = 5
22.104686 - 14.104686 - 3 = 5
5 = 5

- 1.7015621² - 3(- 1.7015621) - 3 = 5
2.895314 + 5.104686 - 3 = 5
5 = 5

x² - 3x - 3 = 5

Subtract 5 from both sides.
x² - 3x - 3 - 5 = 5 - 5
x² - 3x - 8 = 0

Use the quadratic formula.

Given: ax² + bx + c = 0
Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a

Given: 1x² + -3x + -8 = 0
Means: a = 1, b = -3, c = -8

x = [-b ± √(b² - 4ac)] / 2a
x = [-(-3) ± √((-3)² - 4(1)(-8))] / 2(1)
x = [3 ± √(9 + 32)] / 2
x = (3 ± √41) / 2

ANSWER: x = (3 ± √41) / 2

x²-3x-8=0

x=3±√-3²-4(1)(-8)/2(1)
x=3±√9+32/2
x=3±√41/2

question variety a million : For this equation x^2 - 7*x - a million = - 7 , answer here questions : A. discover the roots using Quadratic formulation ! B. Use factorization to discover the basis of the equation ! C. Use polishing off the sq. to discover the basis of the equation ! answer variety a million : First, we'd desire to coach equation : x^2 - 7*x - a million = - 7 , right into a*x^2+b*x+c=0 sort. x^2 - 7*x - a million = - 7 , circulate each and every thing in the sumptuous hand factor, to the left hand edge of the equation <=> x^2 - 7*x - a million - ( - 7 ) = 0 , that's the comparable with <=> x^2 - 7*x - a million + ( 7 ) =0 , now open the bracket and we get <=> x^2 - 7*x + 6 = 0 The equation x^2 - 7*x + 6 = 0 is already in a*x^2+b*x+c=0 sort. In that kind, we are able to actual derive that the cost of a = a million, b = -7, c = 6. 1A. discover the roots using Quadratic formulation ! Use the formulation, x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a) We had be conscious of that a = a million, b = -7 and c = 6, we'd desire to subtitute a,b,c in the abc formulation, with thos values. Which produce x1 = (-(-7) + sqrt( (-7)^2 - 4 * (a million)*(6)))/(2*a million) and x2 = (-(-7) - sqrt( (-7)^2 - 4 * (a million)*(6)))/(2*a million) that's the comparable with x1 = ( 7 + sqrt( 40 9-24))/(2) and x2 = ( 7 - sqrt( 40 9-24))/(2) Which make x1 = ( 7 + sqrt( 25))/(2) and x2 = ( 7 - sqrt( 25))/(2) So we get x1 = ( 7 + 5 )/(2) and x2 = ( 7 - 5 )/(2) So we've the solutions x1 = 6 and x2 = a million 1B. Use factorization to discover the basis of the equation ! x^2 - 7*x + 6 = 0 ( x - 6 ) * ( x - a million ) = 0 The solutions are x1 = 6 and x2 = a million 1C. Use polishing off the sq. to discover the basis of the equation ! x^2 - 7*x + 6 = 0 ,divide the two factor with a million Then we get x^2 - 7*x + 6 = 0 , all of us be conscious of that the coefficient of x is -7 we'd desire to apply the certainty that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = -7/2 = -3.5 So we've make the equation into x^2 - 7*x + 12.25 - 6.25 = 0 that would nicely be grew to become into ( x - 3.5 )^2 - 6.25 = 0 So we are able to get (( x - 3.5 ) - 2.5 ) * (( x - 3.5 ) + 2.5 ) = 0 by using the associative regulation we get ( x - 3.5 - 2.5 ) * ( x - 3.5 + 2.5 ) = 0 And that's the comparable with ( x - 6 ) * ( x - a million ) = 0 So we've been given the solutions as x1 = 6 and x2 = a million

x² - 3x - 8 = 0
x = [ 3 ± √ (9 + 32 ) ] / 2
x = [ 3 ± √ (41) ] / 2

x^2 - 3x - 3 = 5
x^2 - 3x - 3 - 5 = 0
x^2 - 3x - 8 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 1
b = -3
c = -8

x = [3 ±√(9 + 32)]/2
x = [3 ±√41]/2

∴ x = [3 ±√41]/2

equation: 5= x² – 3x – 3
take the 5 to the other side and change the sign (-5).
0= x² – 3x – 3-5
0= x² – 3x – 8

Formula: x= -b ± √b² - 4ac / 2a

0= x² – 3x – 8

a= the number and sign in front of the x² so +1
b= the number in front of the x so -3
c= the left over number so - 8


x= -(-3) ± √-3² - ( 4 ×1 × -8) / (2×1)
^ Becomes positive because two negatives make a positive.

x = 3 ± √9 +32 / 2

x = 3 ± √41 / 2

So now to work out the answerSS.

x= 3 +√41 / 2
x= 4.701562119
x= 4.7

Or

x= 3–√41 / 2
x= -1.701562119
x= -1.7

Hope that's right or help somewhat.

subtract the 5
x^2 - 3x -8
a=1, b= -3, c= -8
3+-rad(9-4(1)(-8)
divided by 2
3+-rad(41)
divided by 2

x^2 - 3x - 8 = 0

3 +/- (9 - 4(1)(-8))^(1/2) /2

3 +/- (9 + 32)^(1/2) /2

3 +/- (41)^1/2 / 2

3/2 +/- (41)^1/2 / 2

subtract 5 from both sides to get:
x^2-3x-8=0
so now just plug the numbers into that quadratic formula:
a=1
b=-3
c=-8