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Simplifying 0 = (2x + -9)(2x + -7) + -1(8x + -5)(5x + -6) Reorder the terms: 0 = (-9 + 2x)(2x + -7) + -1(8x + -5)(5x + -6) Reorder the terms: 0 = (-9 + 2x)(-7 + 2x) + -1(8x + -5)(5x + -6) Multiply (-9 + 2x) * (-7 + 2x) 0 = (-9(-7 + 2x) + 2x * (-7 + 2x)) + -1(8x + -5)(5x + -6) 0 = ((-7 * -9 + 2x * -9) + 2x * (-7 + 2x)) + -1(8x + -5)(5x + -6) 0 = ((63 + -18x) + 2x * (-7 + 2x)) + -1(8x + -5)(5x + -6) 0 = (63 + -18x + (-7 * 2x + 2x * 2x)) + -1(8x + -5)(5x + -6) 0 = (63 + -18x + (-14x + 4x2)) + -1(8x + -5)(5x + -6) Combine like terms: -18x + -14x = -32x 0 = (63 + -32x + 4x2) + -1(8x + -5)(5x + -6) Reorder the terms: 0 = 63 + -32x + 4x2 + -1(-5 + 8x)(5x + -6) Reorder the terms: 0 = 63 + -32x + 4x2 + -1(-5 + 8x)(-6 + 5x) Multiply (-5 + 8x) * (-6 + 5x) 0 = 63 + -32x + 4x2 + -1(-5(-6 + 5x) + 8x * (-6 + 5x)) 0 = 63 + -32x + 4x2 + -1((-6 * -5 + 5x * -5) + 8x * (-6 + 5x)) 0 = 63 + -32x + 4x2 + -1((30 + -25x) + 8x * (-6 + 5x)) 0 = 63 + -32x + 4x2 + -1(30 + -25x + (-6 * 8x + 5x * 8x)) 0 = 63 + -32x + 4x2 + -1(30 + -25x + (-48x + 40x2)) Combine like terms: -25x + -48x = -73x 0 = 63 + -32x + 4x2 + -1(30 + -73x + 40x2) 0 = 63 + -32x + 4x2 + (30 * -1 + -73x * -1 + 40x2 * -1) 0 = 63 + -32x + 4x2 + (-30 + 73x + -40x2) Reorder the terms: 0 = 63 + -30 + -32x + 73x + 4x2 + -40x2 Combine like terms: 63 + -30 = 33 0 = 33 + -32x + 73x + 4x2 + -40x2 Combine like terms: -32x + 73x = 41x 0 = 33 + 41x + 4x2 + -40x2 Combine like terms: 4x2 + -40x2 = -36x2 0 = 33 + 41x + -36x2 Solving 0 = 33 + 41x + -36x2 Solving for variable 'x'. Combine like terms: 0 + -33 = -33 -33 + -41x + 36x2 = 33 + 41x + -36x2 + -33 + -41x + 36x2 Reorder the terms: -33 + -41x + 36x2 = 33 + -33 + 41x + -41x + -36x2 + 36x2 Combine like terms: 33 + -33 = 0 -33 + -41x + 36x2 = 0 + 41x + -41x + -36x2 + 36x2 -33 + -41x + 36x2 = 41x + -41x + -36x2 + 36x2 Combine like terms: 41x + -41x = 0 -33 + -41x + 36x2 = 0 + -36x2 + 36x2 -33 + -41x + 36x2 = -36x2 + 36x2 Combine like terms: -36x2 + 36x2 = 0 -33 + -41x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.9166666667 + -1.138888889x + x2 = 0 Move the constant term to the right: Add '0.9166666667' to each side of the equation. -0.9166666667 + -1.138888889x + 0.9166666667 + x2 = 0 + 0.9166666667 Reorder the terms: -0.9166666667 + 0.9166666667 + -1.138888889x + x2 = 0 + 0.9166666667 Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000 0.0000000000 + -1.138888889x + x2 = 0 + 0.9166666667 -1.138888889x + x2 = 0 + 0.9166666667 Combine like terms: 0 + 0.9166666667 = 0.9166666667 -1.138888889x + x2 = 0.9166666667 The x term is -1.138888889x. Take half its coefficient (-0.5694444445). Square it (0.3242669754) and add it to both sides. Add '0.3242669754' to each side of the equation. -1.138888889x + 0.3242669754 + x2 = 0.9166666667 + 0.3242669754 Reorder the terms: 0.3242669754 + -1.138888889x + x2 = 0.9166666667 + 0.3242669754 Combine like terms: 0.9166666667 + 0.3242669754 = 1.2409336421 0.3242669754 + -1.138888889x + x2 = 1.2409336421 Factor a perfect square on the left side: (x + -0.5694444445)(x + -0.5694444445) = 1.2409336421 Calculate the square root of the right side: 1.113972011 Break this problem into two subproblems by setting (x + -0.5694444445) equal to 1.113972011 and -1.113972011.Subproblem 1
x + -0.5694444445 = 1.113972011 Simplifying x + -0.5694444445 = 1.113972011 Reorder the terms: -0.5694444445 + x = 1.113972011 Solving -0.5694444445 + x = 1.113972011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5694444445' to each side of the equation. -0.5694444445 + 0.5694444445 + x = 1.113972011 + 0.5694444445 Combine like terms: -0.5694444445 + 0.5694444445 = 0.0000000000 0.0000000000 + x = 1.113972011 + 0.5694444445 x = 1.113972011 + 0.5694444445 Combine like terms: 1.113972011 + 0.5694444445 = 1.6834164555 x = 1.6834164555 Simplifying x = 1.6834164555Subproblem 2
x + -0.5694444445 = -1.113972011 Simplifying x + -0.5694444445 = -1.113972011 Reorder the terms: -0.5694444445 + x = -1.113972011 Solving -0.5694444445 + x = -1.113972011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5694444445' to each side of the equation. -0.5694444445 + 0.5694444445 + x = -1.113972011 + 0.5694444445 Combine like terms: -0.5694444445 + 0.5694444445 = 0.0000000000 0.0000000000 + x = -1.113972011 + 0.5694444445 x = -1.113972011 + 0.5694444445 Combine like terms: -1.113972011 + 0.5694444445 = -0.5445275665 x = -0.5445275665 Simplifying x = -0.5445275665Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6834164555, -0.5445275665}
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