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Simplifying 2x2 + -2x + -175 = 0 Reorder the terms: -175 + -2x + 2x2 = 0 Solving -175 + -2x + 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'. -87.5 + -1x + x2 = 0 Move the constant term to the right: Add '87.5' to each side of the equation. -87.5 + -1x + 87.5 + x2 = 0 + 87.5 Reorder the terms: -87.5 + 87.5 + -1x + x2 = 0 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + -1x + x2 = 0 + 87.5 -1x + x2 = 0 + 87.5 Combine like terms: 0 + 87.5 = 87.5 -1x + x2 = 87.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 87.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 87.5 + 0.25 Combine like terms: 87.5 + 0.25 = 87.75 0.25 + -1x + x2 = 87.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 87.75 Calculate the square root of the right side: 9.367496998 Break this problem into two subproblems by setting (x + -0.5) equal to 9.367496998 and -9.367496998.Subproblem 1
x + -0.5 = 9.367496998 Simplifying x + -0.5 = 9.367496998 Reorder the terms: -0.5 + x = 9.367496998 Solving -0.5 + x = 9.367496998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 9.367496998 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 9.367496998 + 0.5 x = 9.367496998 + 0.5 Combine like terms: 9.367496998 + 0.5 = 9.867496998 x = 9.867496998 Simplifying x = 9.867496998Subproblem 2
x + -0.5 = -9.367496998 Simplifying x + -0.5 = -9.367496998 Reorder the terms: -0.5 + x = -9.367496998 Solving -0.5 + x = -9.367496998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -9.367496998 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -9.367496998 + 0.5 x = -9.367496998 + 0.5 Combine like terms: -9.367496998 + 0.5 = -8.867496998 x = -8.867496998 Simplifying x = -8.867496998Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.867496998, -8.867496998}
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