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Simplifying -15x + x2 = 99 Solving -15x + x2 = 99 Solving for variable 'x'. Reorder the terms: -99 + -15x + x2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -15x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -15x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -15x + x2 = 0 + 99 -15x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -15x + x2 = 99 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 = 99 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 99 + 56.25 Combine like terms: 99 + 56.25 = 155.25 56.25 + -15x + x2 = 155.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 155.25 Calculate the square root of the right side: 12.459935794 Break this problem into two subproblems by setting (x + -7.5) equal to 12.459935794 and -12.459935794.Subproblem 1
x + -7.5 = 12.459935794 Simplifying x + -7.5 = 12.459935794 Reorder the terms: -7.5 + x = 12.459935794 Solving -7.5 + x = 12.459935794 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 = 12.459935794 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 12.459935794 + 7.5 x = 12.459935794 + 7.5 Combine like terms: 12.459935794 + 7.5 = 19.959935794 x = 19.959935794 Simplifying x = 19.959935794Subproblem 2
x + -7.5 = -12.459935794 Simplifying x + -7.5 = -12.459935794 Reorder the terms: -7.5 + x = -12.459935794 Solving -7.5 + x = -12.459935794 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 = -12.459935794 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -12.459935794 + 7.5 x = -12.459935794 + 7.5 Combine like terms: -12.459935794 + 7.5 = -4.959935794 x = -4.959935794 Simplifying x = -4.959935794Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.959935794, -4.959935794}
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