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Simplifying 0 = 2x2 + -7x + -175 Reorder the terms: 0 = -175 + -7x + 2x2 Solving 0 = -175 + -7x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 175 = 175 175 + 7x + -2x2 = -175 + -7x + 2x2 + 175 + 7x + -2x2 Reorder the terms: 175 + 7x + -2x2 = -175 + 175 + -7x + 7x + 2x2 + -2x2 Combine like terms: -175 + 175 = 0 175 + 7x + -2x2 = 0 + -7x + 7x + 2x2 + -2x2 175 + 7x + -2x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 175 + 7x + -2x2 = 0 + 2x2 + -2x2 175 + 7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 175 + 7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -87.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '87.5' to each side of the equation. -87.5 + -3.5x + 87.5 + x2 = 0 + 87.5 Reorder the terms: -87.5 + 87.5 + -3.5x + x2 = 0 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + -3.5x + x2 = 0 + 87.5 -3.5x + x2 = 0 + 87.5 Combine like terms: 0 + 87.5 = 87.5 -3.5x + x2 = 87.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 87.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 87.5 + 3.0625 Combine like terms: 87.5 + 3.0625 = 90.5625 3.0625 + -3.5x + x2 = 90.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 90.5625 Calculate the square root of the right side: 9.516433155 Break this problem into two subproblems by setting (x + -1.75) equal to 9.516433155 and -9.516433155.Subproblem 1
x + -1.75 = 9.516433155 Simplifying x + -1.75 = 9.516433155 Reorder the terms: -1.75 + x = 9.516433155 Solving -1.75 + x = 9.516433155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 9.516433155 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 9.516433155 + 1.75 x = 9.516433155 + 1.75 Combine like terms: 9.516433155 + 1.75 = 11.266433155 x = 11.266433155 Simplifying x = 11.266433155Subproblem 2
x + -1.75 = -9.516433155 Simplifying x + -1.75 = -9.516433155 Reorder the terms: -1.75 + x = -9.516433155 Solving -1.75 + x = -9.516433155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -9.516433155 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -9.516433155 + 1.75 x = -9.516433155 + 1.75 Combine like terms: -9.516433155 + 1.75 = -7.766433155 x = -7.766433155 Simplifying x = -7.766433155Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.266433155, -7.766433155}
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