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Simplifying 2x2 + 8x + -144 = 0 Reorder the terms: -144 + 8x + 2x2 = 0 Solving -144 + 8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-72 + 4x + x2)' equal to zero and attempt to solve: Simplifying -72 + 4x + x2 = 0 Solving -72 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 4x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 4x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 4x + x2 = 0 + 72 4x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 4x + x2 = 72 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 72 + 4 Reorder the terms: 4 + 4x + x2 = 72 + 4 Combine like terms: 72 + 4 = 76 4 + 4x + x2 = 76 Factor a perfect square on the left side: (x + 2)(x + 2) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (x + 2) equal to 8.717797887 and -8.717797887.Subproblem 1
x + 2 = 8.717797887 Simplifying x + 2 = 8.717797887 Reorder the terms: 2 + x = 8.717797887 Solving 2 + x = 8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 8.717797887 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.717797887 + -2 x = 8.717797887 + -2 Combine like terms: 8.717797887 + -2 = 6.717797887 x = 6.717797887 Simplifying x = 6.717797887Subproblem 2
x + 2 = -8.717797887 Simplifying x + 2 = -8.717797887 Reorder the terms: 2 + x = -8.717797887 Solving 2 + x = -8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -8.717797887 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.717797887 + -2 x = -8.717797887 + -2 Combine like terms: -8.717797887 + -2 = -10.717797887 x = -10.717797887 Simplifying x = -10.717797887Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.717797887, -10.717797887}Solution
x = {6.717797887, -10.717797887}
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