-(x+2)(x+12)=5x+4

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Solution for -(x+2)(x+12)=5x+4 equation:


Simplifying
-1(x + 2)(x + 12) = 5x + 4

Reorder the terms:
-1(2 + x)(x + 12) = 5x + 4

Reorder the terms:
-1(2 + x)(12 + x) = 5x + 4

Multiply (2 + x) * (12 + x)
-1(2(12 + x) + x(12 + x)) = 5x + 4
-1((12 * 2 + x * 2) + x(12 + x)) = 5x + 4
-1((24 + 2x) + x(12 + x)) = 5x + 4
-1(24 + 2x + (12 * x + x * x)) = 5x + 4
-1(24 + 2x + (12x + x2)) = 5x + 4

Combine like terms: 2x + 12x = 14x
-1(24 + 14x + x2) = 5x + 4
(24 * -1 + 14x * -1 + x2 * -1) = 5x + 4
(-24 + -14x + -1x2) = 5x + 4

Reorder the terms:
-24 + -14x + -1x2 = 4 + 5x

Solving
-24 + -14x + -1x2 = 4 + 5x

Solving for variable 'x'.

Reorder the terms:
-24 + -4 + -14x + -5x + -1x2 = 4 + 5x + -4 + -5x

Combine like terms: -24 + -4 = -28
-28 + -14x + -5x + -1x2 = 4 + 5x + -4 + -5x

Combine like terms: -14x + -5x = -19x
-28 + -19x + -1x2 = 4 + 5x + -4 + -5x

Reorder the terms:
-28 + -19x + -1x2 = 4 + -4 + 5x + -5x

Combine like terms: 4 + -4 = 0
-28 + -19x + -1x2 = 0 + 5x + -5x
-28 + -19x + -1x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-28 + -19x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(28 + 19x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(28 + 19x + x2)' equal to zero and attempt to solve: Simplifying 28 + 19x + x2 = 0 Solving 28 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + 19x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + 19x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 19x + x2 = 0 + -28 19x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 19x + x2 = -28 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -28 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -28 + 90.25 Combine like terms: -28 + 90.25 = 62.25 90.25 + 19x + x2 = 62.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + 9.5) equal to 7.889866919 and -7.889866919.

Subproblem 1

x + 9.5 = 7.889866919 Simplifying x + 9.5 = 7.889866919 Reorder the terms: 9.5 + x = 7.889866919 Solving 9.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 7.889866919 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 7.889866919 + -9.5 x = 7.889866919 + -9.5 Combine like terms: 7.889866919 + -9.5 = -1.610133081 x = -1.610133081 Simplifying x = -1.610133081

Subproblem 2

x + 9.5 = -7.889866919 Simplifying x + 9.5 = -7.889866919 Reorder the terms: 9.5 + x = -7.889866919 Solving 9.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -7.889866919 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -7.889866919 + -9.5 x = -7.889866919 + -9.5 Combine like terms: -7.889866919 + -9.5 = -17.389866919 x = -17.389866919 Simplifying x = -17.389866919

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.610133081, -17.389866919}

Solution

x = {-1.610133081, -17.389866919}

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