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Simplifying -200x2 + 8800x + -95928 = 0 Reorder the terms: -95928 + 8800x + -200x2 = 0 Solving -95928 + 8800x + -200x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-11991 + 1100x + -25x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-11991 + 1100x + -25x2)' equal to zero and attempt to solve: Simplifying -11991 + 1100x + -25x2 = 0 Solving -11991 + 1100x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. 479.64 + -44x + x2 = 0 Move the constant term to the right: Add '-479.64' to each side of the equation. 479.64 + -44x + -479.64 + x2 = 0 + -479.64 Reorder the terms: 479.64 + -479.64 + -44x + x2 = 0 + -479.64 Combine like terms: 479.64 + -479.64 = 0.00 0.00 + -44x + x2 = 0 + -479.64 -44x + x2 = 0 + -479.64 Combine like terms: 0 + -479.64 = -479.64 -44x + x2 = -479.64 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = -479.64 + 484 Reorder the terms: 484 + -44x + x2 = -479.64 + 484 Combine like terms: -479.64 + 484 = 4.36 484 + -44x + x2 = 4.36 Factor a perfect square on the left side: (x + -22)(x + -22) = 4.36 Calculate the square root of the right side: 2.088061302 Break this problem into two subproblems by setting (x + -22) equal to 2.088061302 and -2.088061302.Subproblem 1
x + -22 = 2.088061302 Simplifying x + -22 = 2.088061302 Reorder the terms: -22 + x = 2.088061302 Solving -22 + x = 2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 2.088061302 + 22 Combine like terms: -22 + 22 = 0 0 + x = 2.088061302 + 22 x = 2.088061302 + 22 Combine like terms: 2.088061302 + 22 = 24.088061302 x = 24.088061302 Simplifying x = 24.088061302Subproblem 2
x + -22 = -2.088061302 Simplifying x + -22 = -2.088061302 Reorder the terms: -22 + x = -2.088061302 Solving -22 + x = -2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -2.088061302 + 22 Combine like terms: -22 + 22 = 0 0 + x = -2.088061302 + 22 x = -2.088061302 + 22 Combine like terms: -2.088061302 + 22 = 19.911938698 x = 19.911938698 Simplifying x = 19.911938698Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.088061302, 19.911938698}Solution
x = {24.088061302, 19.911938698}
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