(2x+5)(2x+5)=x+13

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Solution for (2x+5)(2x+5)=x+13 equation:


Simplifying
(2x + 5)(2x + 5) = x + 13

Reorder the terms:
(5 + 2x)(2x + 5) = x + 13

Reorder the terms:
(5 + 2x)(5 + 2x) = x + 13

Multiply (5 + 2x) * (5 + 2x)
(5(5 + 2x) + 2x * (5 + 2x)) = x + 13
((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = x + 13
((25 + 10x) + 2x * (5 + 2x)) = x + 13
(25 + 10x + (5 * 2x + 2x * 2x)) = x + 13
(25 + 10x + (10x + 4x2)) = x + 13

Combine like terms: 10x + 10x = 20x
(25 + 20x + 4x2) = x + 13

Reorder the terms:
25 + 20x + 4x2 = 13 + x

Solving
25 + 20x + 4x2 = 13 + x

Solving for variable 'x'.

Reorder the terms:
25 + -13 + 20x + -1x + 4x2 = 13 + x + -13 + -1x

Combine like terms: 25 + -13 = 12
12 + 20x + -1x + 4x2 = 13 + x + -13 + -1x

Combine like terms: 20x + -1x = 19x
12 + 19x + 4x2 = 13 + x + -13 + -1x

Reorder the terms:
12 + 19x + 4x2 = 13 + -13 + x + -1x

Combine like terms: 13 + -13 = 0
12 + 19x + 4x2 = 0 + x + -1x
12 + 19x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
12 + 19x + 4x2 = 0

Factor a trinomial.
(4 + x)(3 + 4x) = 0

Subproblem 1

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75

Solution

x = {-4, -0.75}

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