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Simplifying x2 + -15x + -725 = 0 Reorder the terms: -725 + -15x + x2 = 0 Solving -725 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '725' to each side of the equation. -725 + -15x + 725 + x2 = 0 + 725 Reorder the terms: -725 + 725 + -15x + x2 = 0 + 725 Combine like terms: -725 + 725 = 0 0 + -15x + x2 = 0 + 725 -15x + x2 = 0 + 725 Combine like terms: 0 + 725 = 725 -15x + x2 = 725 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 = 725 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 725 + 56.25 Combine like terms: 725 + 56.25 = 781.25 56.25 + -15x + x2 = 781.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 781.25 Calculate the square root of the right side: 27.950849719 Break this problem into two subproblems by setting (x + -7.5) equal to 27.950849719 and -27.950849719.Subproblem 1
x + -7.5 = 27.950849719 Simplifying x + -7.5 = 27.950849719 Reorder the terms: -7.5 + x = 27.950849719 Solving -7.5 + x = 27.950849719 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 = 27.950849719 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 27.950849719 + 7.5 x = 27.950849719 + 7.5 Combine like terms: 27.950849719 + 7.5 = 35.450849719 x = 35.450849719 Simplifying x = 35.450849719Subproblem 2
x + -7.5 = -27.950849719 Simplifying x + -7.5 = -27.950849719 Reorder the terms: -7.5 + x = -27.950849719 Solving -7.5 + x = -27.950849719 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 = -27.950849719 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -27.950849719 + 7.5 x = -27.950849719 + 7.5 Combine like terms: -27.950849719 + 7.5 = -20.450849719 x = -20.450849719 Simplifying x = -20.450849719Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.450849719, -20.450849719}
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