(2x+4)(x)=144

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Solution for (2x+4)(x)=144 equation:


Simplifying
(2x + 4)(x) = 144

Reorder the terms:
(4 + 2x)(x) = 144

Reorder the terms for easier multiplication:
x(4 + 2x) = 144
(4 * x + 2x * x) = 144
(4x + 2x2) = 144

Solving
4x + 2x2 = 144

Solving for variable 'x'.

Reorder the terms:
-144 + 4x + 2x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + 2x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-72 + 2x + x2)' equal to zero and attempt to solve: Simplifying -72 + 2x + x2 = 0 Solving -72 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 2x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 2x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 2x + x2 = 0 + 72 2x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 2x + x2 = 72 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 72 + 1 Reorder the terms: 1 + 2x + x2 = 72 + 1 Combine like terms: 72 + 1 = 73 1 + 2x + x2 = 73 Factor a perfect square on the left side: (x + 1)(x + 1) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 1) equal to 8.544003745 and -8.544003745.

Subproblem 1

x + 1 = 8.544003745 Simplifying x + 1 = 8.544003745 Reorder the terms: 1 + x = 8.544003745 Solving 1 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 8.544003745 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.544003745 + -1 x = 8.544003745 + -1 Combine like terms: 8.544003745 + -1 = 7.544003745 x = 7.544003745 Simplifying x = 7.544003745

Subproblem 2

x + 1 = -8.544003745 Simplifying x + 1 = -8.544003745 Reorder the terms: 1 + x = -8.544003745 Solving 1 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -8.544003745 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.544003745 + -1 x = -8.544003745 + -1 Combine like terms: -8.544003745 + -1 = -9.544003745 x = -9.544003745 Simplifying x = -9.544003745

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.544003745, -9.544003745}

Solution

x = {7.544003745, -9.544003745}

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