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Simplifying 15 = -2x * x + 100x Multiply x * x 15 = -2x^{2}+ 100x Reorder the terms: 15 = 100x + -2x^{2}Solving 15 = 100x + -2x^{2}Solving for variable 'x'. Reorder the terms: 15 + -100x + 2x^{2}= 100x + -100x + -2x^{2}+ 2x^{2}Combine like terms: 100x + -100x = 0 15 + -100x + 2x^{2}= 0 + -2x^{2}+ 2x^{2}15 + -100x + 2x^{2}= -2x^{2}+ 2x^{2}Combine like terms: -2x^{2}+ 2x^{2}= 0 15 + -100x + 2x^{2}= 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -50x + x^{2}= 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -50x + -7.5 + x^{2}= 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -50x + x^{2}= 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -50x + x^{2}= 0 + -7.5 -50x + x^{2}= 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -50x + x^{2}= -7.5 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x^{2}= -7.5 + 625 Reorder the terms: 625 + -50x + x^{2}= -7.5 + 625 Combine like terms: -7.5 + 625 = 617.5 625 + -50x + x^{2}= 617.5 Factor a perfect square on the left side: (x + -25)(x + -25) = 617.5 Calculate the square root of the right side: 24.84954728 Break this problem into two subproblems by setting (x + -25) equal to 24.84954728 and -24.84954728.## Subproblem 1

x + -25 = 24.84954728 Simplifying x + -25 = 24.84954728 Reorder the terms: -25 + x = 24.84954728 Solving -25 + x = 24.84954728 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 24.84954728 + 25 Combine like terms: -25 + 25 = 0 0 + x = 24.84954728 + 25 x = 24.84954728 + 25 Combine like terms: 24.84954728 + 25 = 49.84954728 x = 49.84954728 Simplifying x = 49.84954728## Subproblem 2

x + -25 = -24.84954728 Simplifying x + -25 = -24.84954728 Reorder the terms: -25 + x = -24.84954728 Solving -25 + x = -24.84954728 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -24.84954728 + 25 Combine like terms: -25 + 25 = 0 0 + x = -24.84954728 + 25 x = -24.84954728 + 25 Combine like terms: -24.84954728 + 25 = 0.15045272 x = 0.15045272 Simplifying x = 0.15045272## Solution

The solution to the problem is based on the solutions from the subproblems. x = {49.84954728, 0.15045272}

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