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Simplifying 5x2 + 180x + -360 = 0 Reorder the terms: -360 + 180x + 5x2 = 0 Solving -360 + 180x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-72 + 36x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-72 + 36x + x2)' equal to zero and attempt to solve: Simplifying -72 + 36x + x2 = 0 Solving -72 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 36x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 36x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 36x + x2 = 0 + 72 36x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 36x + x2 = 72 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = 72 + 324 Reorder the terms: 324 + 36x + x2 = 72 + 324 Combine like terms: 72 + 324 = 396 324 + 36x + x2 = 396 Factor a perfect square on the left side: (x + 18)(x + 18) = 396 Calculate the square root of the right side: 19.899748742 Break this problem into two subproblems by setting (x + 18) equal to 19.899748742 and -19.899748742.Subproblem 1
x + 18 = 19.899748742 Simplifying x + 18 = 19.899748742 Reorder the terms: 18 + x = 19.899748742 Solving 18 + x = 19.899748742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 19.899748742 + -18 Combine like terms: 18 + -18 = 0 0 + x = 19.899748742 + -18 x = 19.899748742 + -18 Combine like terms: 19.899748742 + -18 = 1.899748742 x = 1.899748742 Simplifying x = 1.899748742Subproblem 2
x + 18 = -19.899748742 Simplifying x + 18 = -19.899748742 Reorder the terms: 18 + x = -19.899748742 Solving 18 + x = -19.899748742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -19.899748742 + -18 Combine like terms: 18 + -18 = 0 0 + x = -19.899748742 + -18 x = -19.899748742 + -18 Combine like terms: -19.899748742 + -18 = -37.899748742 x = -37.899748742 Simplifying x = -37.899748742Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.899748742, -37.899748742}Solution
x = {1.899748742, -37.899748742}
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