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Simplifying 2x2 + -30x + -475 = 0 Reorder the terms: -475 + -30x + 2x2 = 0 Solving -475 + -30x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -237.5 + -15x + x2 = 0 Move the constant term to the right: Add '237.5' to each side of the equation. -237.5 + -15x + 237.5 + x2 = 0 + 237.5 Reorder the terms: -237.5 + 237.5 + -15x + x2 = 0 + 237.5 Combine like terms: -237.5 + 237.5 = 0.0 0.0 + -15x + x2 = 0 + 237.5 -15x + x2 = 0 + 237.5 Combine like terms: 0 + 237.5 = 237.5 -15x + x2 = 237.5 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 = 237.5 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 237.5 + 56.25 Combine like terms: 237.5 + 56.25 = 293.75 56.25 + -15x + x2 = 293.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 293.75 Calculate the square root of the right side: 17.139136501 Break this problem into two subproblems by setting (x + -7.5) equal to 17.139136501 and -17.139136501.Subproblem 1
x + -7.5 = 17.139136501 Simplifying x + -7.5 = 17.139136501 Reorder the terms: -7.5 + x = 17.139136501 Solving -7.5 + x = 17.139136501 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 = 17.139136501 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 17.139136501 + 7.5 x = 17.139136501 + 7.5 Combine like terms: 17.139136501 + 7.5 = 24.639136501 x = 24.639136501 Simplifying x = 24.639136501Subproblem 2
x + -7.5 = -17.139136501 Simplifying x + -7.5 = -17.139136501 Reorder the terms: -7.5 + x = -17.139136501 Solving -7.5 + x = -17.139136501 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 = -17.139136501 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -17.139136501 + 7.5 x = -17.139136501 + 7.5 Combine like terms: -17.139136501 + 7.5 = -9.639136501 x = -9.639136501 Simplifying x = -9.639136501Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.639136501, -9.639136501}
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