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Simplifying x2 + -15x + -110 = 0 Reorder the terms: -110 + -15x + x2 = 0 Solving -110 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + -15x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + -15x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + -15x + x2 = 0 + 110 -15x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 -15x + x2 = 110 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 = 110 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 110 + 56.25 Combine like terms: 110 + 56.25 = 166.25 56.25 + -15x + x2 = 166.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 166.25 Calculate the square root of the right side: 12.893796958 Break this problem into two subproblems by setting (x + -7.5) equal to 12.893796958 and -12.893796958.Subproblem 1
x + -7.5 = 12.893796958 Simplifying x + -7.5 = 12.893796958 Reorder the terms: -7.5 + x = 12.893796958 Solving -7.5 + x = 12.893796958 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 = 12.893796958 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 12.893796958 + 7.5 x = 12.893796958 + 7.5 Combine like terms: 12.893796958 + 7.5 = 20.393796958 x = 20.393796958 Simplifying x = 20.393796958Subproblem 2
x + -7.5 = -12.893796958 Simplifying x + -7.5 = -12.893796958 Reorder the terms: -7.5 + x = -12.893796958 Solving -7.5 + x = -12.893796958 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 = -12.893796958 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -12.893796958 + 7.5 x = -12.893796958 + 7.5 Combine like terms: -12.893796958 + 7.5 = -5.393796958 x = -5.393796958 Simplifying x = -5.393796958Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.393796958, -5.393796958}
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