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Simplifying -4x2 + 550x + 8500 = 0 Reorder the terms: 8500 + 550x + -4x2 = 0 Solving 8500 + 550x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4250 + 275x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4250 + 275x + -2x2)' equal to zero and attempt to solve: Simplifying 4250 + 275x + -2x2 = 0 Solving 4250 + 275x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2125 + -137.5x + x2 = 0 Move the constant term to the right: Add '2125' to each side of the equation. -2125 + -137.5x + 2125 + x2 = 0 + 2125 Reorder the terms: -2125 + 2125 + -137.5x + x2 = 0 + 2125 Combine like terms: -2125 + 2125 = 0 0 + -137.5x + x2 = 0 + 2125 -137.5x + x2 = 0 + 2125 Combine like terms: 0 + 2125 = 2125 -137.5x + x2 = 2125 The x term is -137.5x. Take half its coefficient (-68.75). Square it (4726.5625) and add it to both sides. Add '4726.5625' to each side of the equation. -137.5x + 4726.5625 + x2 = 2125 + 4726.5625 Reorder the terms: 4726.5625 + -137.5x + x2 = 2125 + 4726.5625 Combine like terms: 2125 + 4726.5625 = 6851.5625 4726.5625 + -137.5x + x2 = 6851.5625 Factor a perfect square on the left side: (x + -68.75)(x + -68.75) = 6851.5625 Calculate the square root of the right side: 82.774165656 Break this problem into two subproblems by setting (x + -68.75) equal to 82.774165656 and -82.774165656.Subproblem 1
x + -68.75 = 82.774165656 Simplifying x + -68.75 = 82.774165656 Reorder the terms: -68.75 + x = 82.774165656 Solving -68.75 + x = 82.774165656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68.75' to each side of the equation. -68.75 + 68.75 + x = 82.774165656 + 68.75 Combine like terms: -68.75 + 68.75 = 0.00 0.00 + x = 82.774165656 + 68.75 x = 82.774165656 + 68.75 Combine like terms: 82.774165656 + 68.75 = 151.524165656 x = 151.524165656 Simplifying x = 151.524165656Subproblem 2
x + -68.75 = -82.774165656 Simplifying x + -68.75 = -82.774165656 Reorder the terms: -68.75 + x = -82.774165656 Solving -68.75 + x = -82.774165656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68.75' to each side of the equation. -68.75 + 68.75 + x = -82.774165656 + 68.75 Combine like terms: -68.75 + 68.75 = 0.00 0.00 + x = -82.774165656 + 68.75 x = -82.774165656 + 68.75 Combine like terms: -82.774165656 + 68.75 = -14.024165656 x = -14.024165656 Simplifying x = -14.024165656Solution
The solution to the problem is based on the solutions from the subproblems. x = {151.524165656, -14.024165656}Solution
x = {151.524165656, -14.024165656}
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