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Simplifying 0 = -2x2 + 30x + 87.5 Reorder the terms: 0 = 87.5 + 30x + -2x2 Solving 0 = 87.5 + 30x + -2x2 Solving for variable 'x'. Combine like terms: 0 + -87.5 = -87.5 -87.5 + -30x + 2x2 = 87.5 + 30x + -2x2 + -87.5 + -30x + 2x2 Reorder the terms: -87.5 + -30x + 2x2 = 87.5 + -87.5 + 30x + -30x + -2x2 + 2x2 Combine like terms: 87.5 + -87.5 = 0.0 -87.5 + -30x + 2x2 = 0.0 + 30x + -30x + -2x2 + 2x2 -87.5 + -30x + 2x2 = 30x + -30x + -2x2 + 2x2 Combine like terms: 30x + -30x = 0 -87.5 + -30x + 2x2 = 0 + -2x2 + 2x2 -87.5 + -30x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -87.5 + -30x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -43.75 + -15x + x2 = 0 Move the constant term to the right: Add '43.75' to each side of the equation. -43.75 + -15x + 43.75 + x2 = 0 + 43.75 Reorder the terms: -43.75 + 43.75 + -15x + x2 = 0 + 43.75 Combine like terms: -43.75 + 43.75 = 0.00 0.00 + -15x + x2 = 0 + 43.75 -15x + x2 = 0 + 43.75 Combine like terms: 0 + 43.75 = 43.75 -15x + x2 = 43.75 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 = 43.75 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 43.75 + 56.25 Combine like terms: 43.75 + 56.25 = 100 56.25 + -15x + x2 = 100 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (x + -7.5) equal to 10 and -10.Subproblem 1
x + -7.5 = 10 Simplifying x + -7.5 = 10 Reorder the terms: -7.5 + x = 10 Solving -7.5 + x = 10 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 = 10 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 10 + 7.5 x = 10 + 7.5 Combine like terms: 10 + 7.5 = 17.5 x = 17.5 Simplifying x = 17.5Subproblem 2
x + -7.5 = -10 Simplifying x + -7.5 = -10 Reorder the terms: -7.5 + x = -10 Solving -7.5 + x = -10 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 = -10 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -10 + 7.5 x = -10 + 7.5 Combine like terms: -10 + 7.5 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.5, -2.5}
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