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Simplifying 32 = 4x2 + -89x + 501 Reorder the terms: 32 = 501 + -89x + 4x2 Solving 32 = 501 + -89x + 4x2 Solving for variable 'x'. Combine like terms: 32 + -501 = -469 -469 + 89x + -4x2 = 501 + -89x + 4x2 + -501 + 89x + -4x2 Reorder the terms: -469 + 89x + -4x2 = 501 + -501 + -89x + 89x + 4x2 + -4x2 Combine like terms: 501 + -501 = 0 -469 + 89x + -4x2 = 0 + -89x + 89x + 4x2 + -4x2 -469 + 89x + -4x2 = -89x + 89x + 4x2 + -4x2 Combine like terms: -89x + 89x = 0 -469 + 89x + -4x2 = 0 + 4x2 + -4x2 -469 + 89x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -469 + 89x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 117.25 + -22.25x + x2 = 0 Move the constant term to the right: Add '-117.25' to each side of the equation. 117.25 + -22.25x + -117.25 + x2 = 0 + -117.25 Reorder the terms: 117.25 + -117.25 + -22.25x + x2 = 0 + -117.25 Combine like terms: 117.25 + -117.25 = 0.00 0.00 + -22.25x + x2 = 0 + -117.25 -22.25x + x2 = 0 + -117.25 Combine like terms: 0 + -117.25 = -117.25 -22.25x + x2 = -117.25 The x term is -22.25x. Take half its coefficient (-11.125). Square it (123.765625) and add it to both sides. Add '123.765625' to each side of the equation. -22.25x + 123.765625 + x2 = -117.25 + 123.765625 Reorder the terms: 123.765625 + -22.25x + x2 = -117.25 + 123.765625 Combine like terms: -117.25 + 123.765625 = 6.515625 123.765625 + -22.25x + x2 = 6.515625 Factor a perfect square on the left side: (x + -11.125)(x + -11.125) = 6.515625 Calculate the square root of the right side: 2.552572232 Break this problem into two subproblems by setting (x + -11.125) equal to 2.552572232 and -2.552572232.Subproblem 1
x + -11.125 = 2.552572232 Simplifying x + -11.125 = 2.552572232 Reorder the terms: -11.125 + x = 2.552572232 Solving -11.125 + x = 2.552572232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.125' to each side of the equation. -11.125 + 11.125 + x = 2.552572232 + 11.125 Combine like terms: -11.125 + 11.125 = 0.000 0.000 + x = 2.552572232 + 11.125 x = 2.552572232 + 11.125 Combine like terms: 2.552572232 + 11.125 = 13.677572232 x = 13.677572232 Simplifying x = 13.677572232Subproblem 2
x + -11.125 = -2.552572232 Simplifying x + -11.125 = -2.552572232 Reorder the terms: -11.125 + x = -2.552572232 Solving -11.125 + x = -2.552572232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.125' to each side of the equation. -11.125 + 11.125 + x = -2.552572232 + 11.125 Combine like terms: -11.125 + 11.125 = 0.000 0.000 + x = -2.552572232 + 11.125 x = -2.552572232 + 11.125 Combine like terms: -2.552572232 + 11.125 = 8.572427768 x = 8.572427768 Simplifying x = 8.572427768Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.677572232, 8.572427768}
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