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Simplifying x2 + 15x + -72 = 0 Reorder the terms: -72 + 15x + x2 = 0 Solving -72 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 15x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 15x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 15x + x2 = 0 + 72 15x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 15x + x2 = 72 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 72 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 72 + 56.25 Combine like terms: 72 + 56.25 = 128.25 56.25 + 15x + x2 = 128.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 128.25 Calculate the square root of the right side: 11.324751653 Break this problem into two subproblems by setting (x + 7.5) equal to 11.324751653 and -11.324751653.Subproblem 1
x + 7.5 = 11.324751653 Simplifying x + 7.5 = 11.324751653 Reorder the terms: 7.5 + x = 11.324751653 Solving 7.5 + x = 11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 11.324751653 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 11.324751653 + -7.5 x = 11.324751653 + -7.5 Combine like terms: 11.324751653 + -7.5 = 3.824751653 x = 3.824751653 Simplifying x = 3.824751653Subproblem 2
x + 7.5 = -11.324751653 Simplifying x + 7.5 = -11.324751653 Reorder the terms: 7.5 + x = -11.324751653 Solving 7.5 + x = -11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -11.324751653 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -11.324751653 + -7.5 x = -11.324751653 + -7.5 Combine like terms: -11.324751653 + -7.5 = -18.824751653 x = -18.824751653 Simplifying x = -18.824751653Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.824751653, -18.824751653}
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