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Simplifying x2 = 15x + 80 Reorder the terms: x2 = 80 + 15x Solving x2 = 80 + 15x Solving for variable 'x'. Reorder the terms: -80 + -15x + x2 = 80 + 15x + -80 + -15x Reorder the terms: -80 + -15x + x2 = 80 + -80 + 15x + -15x Combine like terms: 80 + -80 = 0 -80 + -15x + x2 = 0 + 15x + -15x -80 + -15x + x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -80 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -15x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -15x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -15x + x2 = 0 + 80 -15x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -15x + x2 = 80 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 = 80 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 80 + 56.25 Combine like terms: 80 + 56.25 = 136.25 56.25 + -15x + x2 = 136.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 136.25 Calculate the square root of the right side: 11.67261753 Break this problem into two subproblems by setting (x + -7.5) equal to 11.67261753 and -11.67261753.Subproblem 1
x + -7.5 = 11.67261753 Simplifying x + -7.5 = 11.67261753 Reorder the terms: -7.5 + x = 11.67261753 Solving -7.5 + x = 11.67261753 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 = 11.67261753 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 11.67261753 + 7.5 x = 11.67261753 + 7.5 Combine like terms: 11.67261753 + 7.5 = 19.17261753 x = 19.17261753 Simplifying x = 19.17261753Subproblem 2
x + -7.5 = -11.67261753 Simplifying x + -7.5 = -11.67261753 Reorder the terms: -7.5 + x = -11.67261753 Solving -7.5 + x = -11.67261753 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 = -11.67261753 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -11.67261753 + 7.5 x = -11.67261753 + 7.5 Combine like terms: -11.67261753 + 7.5 = -4.17261753 x = -4.17261753 Simplifying x = -4.17261753Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.17261753, -4.17261753}
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