Can you help me solve 2x^2 - 10x = 32?

2x^2 - 10x = 32
2(x^2 - 5x) = 2(16)
x^2 - 5x - 16 = 0
x = [-b ± √(b^2 - 4ac)]/(2a)

a = 1
b = -5
c = -16

x = [5 ± √(25 + 64)]/2
x = [5 ± √89]/2

∴ x = [5 ± √89]/2

2x^2 - 10x - 32 = 0
x^2 - 5x - 16 = 0
x = (-b +/-SQRT(b^2 - 4ac))/2a
x = (5 +/-SQRT(25 + 64))/2 = 7.22, -2.22

2x^2 - 10x - 32 = 0

Compare to standard quadratic: ax^2 + bx + c = 0, so a = 2, b = -10, c = -32

Plug those values into the standard quadratic formula: x = [-b +- sqrt(b^2 - 4ac)] / 2a

2x^2-10x=32

2x^2-10x-32=0

a=2 b=-10 c=-32

-(-10)+/- sq rt -10^2-4(2)(-32)/4

x=10+/- sq rt 100+256/4
x=10+/- sq rt 4 * sq rt 89/4
x=10+/- 2 sq rt 89/4
x=5+/- sq rt 89/2

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METHOD: QUADRATIC FORMULA
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2x² - 10x = 32

Subtract 32 from both sides.
2x² - 10x - 32 = 0

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

Given: 2x² - 10x - 32 = 0
Means: a = 2, b = -10, c = -32

x = [-b ± √(b² - 4ac)] / 2a
x = [-(-10) ± √((-10)² - 4(2)(-32))] / 2(2)
x = [10 ± √(100 + 256)] / 4
x = [10 ± √356] / 4
x = [10 ± √(4 * 89)] / 4
x = (10 ± 2√89) / 4
x = (5 ± √89) / 2

ANSWER: x = (5 ± √89) / 2

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METHOD: COMPLETING THE SQUARE
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2x² - 10x = 32

Factor.
2(x² - 5x) = 32

Add placeholders.
2(x² - 5x + ____) = 32 + 2(____)

Notice that the second placeholder is multiplied by 2 to balance out the 2 you factored out.

Take the coefficient of the x term: -5
Divide it by 2: -5 / 2
Square it: (-5 / 2)² = (25 / 4)

Put (25 / 4) into both placeholders.
2[x² - 5x + (25 / 4)] = 32 + 2(25 / 4)

Simplify the RHS.
2[x² - 5x + (25 / 4)] = 32(4 / 4) + 2(25 / 4)
2[x² - 5x + (25 / 4)] = (128 / 4) + (50 / 4)
2[x² - 5x + (25 / 4)] = (128 + 50) / 4
2[x² - 5x + (25 / 4)] = (178 / 4)

x² - 5x + (25 / 4) is a perfect square.
2[x - (5 / 2)]² = (178 / 4)

Divide both sides by 2.
2[x - (5 / 2)]² / 2 = (178 / 4) / 2
[x - (5 / 2)]² = (178 / 8)
[x - (5 / 2)]² = (89 / 4)

Take the square root of both sides.
√[x - (5 / 2)]² = √(89 / 4)
x - (5 / 2) = ± (√89 / 2)

Add (5 / 2) to both sides.
x - (5 / 2) + (5 / 2) = (5 / 2) ± (√89 / 2)
x = (5 / 2) ± (√89 / 2)
x = (5 ± √89) / 2

ANSWER: x = (5 ± √89) / 2

x^2 - 5x - 32 = 0

x = 5 (+ or -) sq rt (25 + 128) / 2
= 5 (+ or -) sq rt (153) / 2


work it out


Are you sure you don't have a number wrong?