4x(x+30)=180

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Solution for 4x(x+30)=180 equation:


Simplifying
4x(x + 30) = 180

Reorder the terms:
4x(30 + x) = 180
(30 * 4x + x * 4x) = 180
(120x + 4x2) = 180

Solving
120x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 120x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 120x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + 30x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-45 + 30x + x2)' equal to zero and attempt to solve: Simplifying -45 + 30x + x2 = 0 Solving -45 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 30x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 30x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 30x + x2 = 0 + 45 30x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 30x + x2 = 45 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 45 + 225 Reorder the terms: 225 + 30x + x2 = 45 + 225 Combine like terms: 45 + 225 = 270 225 + 30x + x2 = 270 Factor a perfect square on the left side: (x + 15)(x + 15) = 270 Calculate the square root of the right side: 16.431676725 Break this problem into two subproblems by setting (x + 15) equal to 16.431676725 and -16.431676725.

Subproblem 1

x + 15 = 16.431676725 Simplifying x + 15 = 16.431676725 Reorder the terms: 15 + x = 16.431676725 Solving 15 + x = 16.431676725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 16.431676725 + -15 Combine like terms: 15 + -15 = 0 0 + x = 16.431676725 + -15 x = 16.431676725 + -15 Combine like terms: 16.431676725 + -15 = 1.431676725 x = 1.431676725 Simplifying x = 1.431676725

Subproblem 2

x + 15 = -16.431676725 Simplifying x + 15 = -16.431676725 Reorder the terms: 15 + x = -16.431676725 Solving 15 + x = -16.431676725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -16.431676725 + -15 Combine like terms: 15 + -15 = 0 0 + x = -16.431676725 + -15 x = -16.431676725 + -15 Combine like terms: -16.431676725 + -15 = -31.431676725 x = -31.431676725 Simplifying x = -31.431676725

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.431676725, -31.431676725}

Solution

x = {1.431676725, -31.431676725}

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