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Simplifying 0 = -0.0001x2 + 0.0175x + 0.3225 Reorder the terms: 0 = 0.3225 + 0.0175x + -0.0001x2 Solving 0 = 0.3225 + 0.0175x + -0.0001x2 Solving for variable 'x'. Combine like terms: 0 + -0.3225 = -0.3225 -0.3225 + -0.0175x + 0.0001x2 = 0.3225 + 0.0175x + -0.0001x2 + -0.3225 + -0.0175x + 0.0001x2 Reorder the terms: -0.3225 + -0.0175x + 0.0001x2 = 0.3225 + -0.3225 + 0.0175x + -0.0175x + -0.0001x2 + 0.0001x2 Combine like terms: 0.3225 + -0.3225 = 0.0000 -0.3225 + -0.0175x + 0.0001x2 = 0.0000 + 0.0175x + -0.0175x + -0.0001x2 + 0.0001x2 -0.3225 + -0.0175x + 0.0001x2 = 0.0175x + -0.0175x + -0.0001x2 + 0.0001x2 Combine like terms: 0.0175x + -0.0175x = 0.0000 -0.3225 + -0.0175x + 0.0001x2 = 0.0000 + -0.0001x2 + 0.0001x2 -0.3225 + -0.0175x + 0.0001x2 = -0.0001x2 + 0.0001x2 Combine like terms: -0.0001x2 + 0.0001x2 = 0.0000 -0.3225 + -0.0175x + 0.0001x2 = 0.0000 Begin completing the square. Divide all terms by 0.0001 the coefficient of the squared term: Divide each side by '0.0001'. -3225 + -175x + x2 = 0 Move the constant term to the right: Add '3225' to each side of the equation. -3225 + -175x + 3225 + x2 = 0 + 3225 Reorder the terms: -3225 + 3225 + -175x + x2 = 0 + 3225 Combine like terms: -3225 + 3225 = 0 0 + -175x + x2 = 0 + 3225 -175x + x2 = 0 + 3225 Combine like terms: 0 + 3225 = 3225 -175x + x2 = 3225 The x term is -175x. Take half its coefficient (-87.5). Square it (7656.25) and add it to both sides. Add '7656.25' to each side of the equation. -175x + 7656.25 + x2 = 3225 + 7656.25 Reorder the terms: 7656.25 + -175x + x2 = 3225 + 7656.25 Combine like terms: 3225 + 7656.25 = 10881.25 7656.25 + -175x + x2 = 10881.25 Factor a perfect square on the left side: (x + -87.5)(x + -87.5) = 10881.25 Calculate the square root of the right side: 104.313230225 Break this problem into two subproblems by setting (x + -87.5) equal to 104.313230225 and -104.313230225.Subproblem 1
x + -87.5 = 104.313230225 Simplifying x + -87.5 = 104.313230225 Reorder the terms: -87.5 + x = 104.313230225 Solving -87.5 + x = 104.313230225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '87.5' to each side of the equation. -87.5 + 87.5 + x = 104.313230225 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + x = 104.313230225 + 87.5 x = 104.313230225 + 87.5 Combine like terms: 104.313230225 + 87.5 = 191.813230225 x = 191.813230225 Simplifying x = 191.813230225Subproblem 2
x + -87.5 = -104.313230225 Simplifying x + -87.5 = -104.313230225 Reorder the terms: -87.5 + x = -104.313230225 Solving -87.5 + x = -104.313230225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '87.5' to each side of the equation. -87.5 + 87.5 + x = -104.313230225 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + x = -104.313230225 + 87.5 x = -104.313230225 + 87.5 Combine like terms: -104.313230225 + 87.5 = -16.813230225 x = -16.813230225 Simplifying x = -16.813230225Solution
The solution to the problem is based on the solutions from the subproblems. x = {191.813230225, -16.813230225}
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