(4X*X) + X = 6 solve x?

4x² + x = 6

4x² + x - 6 = 0

Delta = 1² - 4 * 4 * (- 6) = 1 + 96 = 97

x1 = (- 1 - sqr (97)) / 8 ~ - 1.356

x2 = (- 1 + sqr (97)) / 8 ~ 1.106

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(4x * x) + x = 6
4x² + x = 6
x² + 1/4x = 3/2
x² + 1/8x = 3/2 + (1/8)²
x² + 1/8x = 96/64 + 1/64
(x + 1/8)² = 97/64
x + 1/8 = +/- 1.2311072

x = 1.2311072 - 0.125, x = 1.1061072
x = - 1.2311072 - 0.125, x = - 1.3561072

Answer: x = 1.1061072, - 1.3561072

Proof (x = 1.1061072):
(4[1.1061072] * 1.1061072) + 1.1061072 = 6
(4.4244288 * 1.1061072)
4.893893 + 1.106107 = 6
6 = 6

Proof (x = - 1.3561072):
(4[- 1.3561072] * - 1.3561072) + (- 1.3561072) = 6
(- 5.4244288 * - 1.3561072) - 1.3561072 = 6
7.356107 - 1.356107 = 6
6 = 6

To be solved: 4x(x-7)-5x(x-6)=-3 STEP 1: EXPAND 4x(x-7) - 5x(x-6) = -3 4x^2 - 28x - 5x^2+30x = -3 STEP 2: SIMPLIFY basically collect and add the like terms (4x^2 - 5x^2) + (-28x + 30x) + 3 = 0 -x^2 + 2x + 3 = 0 Now this is a quadratic in x STEP 3: SOLVE -x^2 + 2x + 3 = 0 you need to find the factors that would give you a product of -3 and addition of 2 i.e., x1*x2 = -3 (1) x1+x2 = 2 (2) where x1 and x2 are your solutions To mutually satisfy equations (1) and (2) x1 = 3 and x2 = -1 now to check x1*x2 = 3*-1 = -3 x1 + x2 = 3 + (-1) = 2 This now solves your equation for x as x = 3 or -1

4 x ² + x - 6 = 0

x = [ - b ± √ ( b ² - 4 a c ) ] / 2 a

x = [ - 1 ± √ ( 1 + 96 ) ] / 8

x = [ - 1 ± √97 ] / 8

4x^2 + x = 6
4x^2 + x - 6 = 0
x = [-b ±√(b2 - 4ac)]/(2a)

a = 4
b = 1
c = -6

x = [-1 ±√(1 + 96)]/8
x = [-1 ±√97]/8

∴ x = [-1 ±√97]/8

(4X*X) + X = 6
4x^2+x=6
4x^2+x-6=0 divide the equation by 4
x^2+x/4-6/4=0
x^2+x/4=6/4
x^2+x/4+1/64=6/4+1/64
(x+1/8)^2=97/64
x+1/8=±√(97/64)
x=-1/8±√(97)/8
......-1+√(97)......-1-√(97)
x=-----------------,---------------- answer//
..........8.................8

4x^2+x-6=0

D= 1-4*a*-6= 97

x1= (-1 - (97)^1/2) /8

x2=( -1+(97)^1/2)/ 8

4x^2 + x = 6
4x^2 + x - 6 = 0
quadratic formula
(-1 +- sqrt(1^2 - 4(4)(-6))/2(4)
(-1 +- sqt(1+96))/8
(-1 +- sqrt(97))/8

hope that helps

4x^2 + x - 6 = 0

Then just use the formula

ax^2 + bx + c = 0

x = -b +/- sqrt( b2 - 4ac)
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