x^2=4(2x+5)

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Solution for x^2=4(2x+5) equation:


Simplifying
x2 = 4(2x + 5)

Reorder the terms:
x2 = 4(5 + 2x)
x2 = (5 * 4 + 2x * 4)
x2 = (20 + 8x)

Solving
x2 = 20 + 8x

Solving for variable 'x'.

Reorder the terms:
-20 + -8x + x2 = 20 + 8x + -20 + -8x

Reorder the terms:
-20 + -8x + x2 = 20 + -20 + 8x + -8x

Combine like terms: 20 + -20 = 0
-20 + -8x + x2 = 0 + 8x + -8x
-20 + -8x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-20 + -8x + x2 = 0

Factor a trinomial.
(-2 + -1x)(10 + -1x) = 0

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Solution

x = {-2, 10}

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