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Simplifying 8x(2x + -9) = -71 Reorder the terms: 8x(-9 + 2x) = -71 (-9 * 8x + 2x * 8x) = -71 (-72x + 16x2) = -71 Solving -72x + 16x2 = -71 Solving for variable 'x'. Reorder the terms: 71 + -72x + 16x2 = -71 + 71 Combine like terms: -71 + 71 = 0 71 + -72x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 4.4375 + -4.5x + x2 = 0 Move the constant term to the right: Add '-4.4375' to each side of the equation. 4.4375 + -4.5x + -4.4375 + x2 = 0 + -4.4375 Reorder the terms: 4.4375 + -4.4375 + -4.5x + x2 = 0 + -4.4375 Combine like terms: 4.4375 + -4.4375 = 0.0000 0.0000 + -4.5x + x2 = 0 + -4.4375 -4.5x + x2 = 0 + -4.4375 Combine like terms: 0 + -4.4375 = -4.4375 -4.5x + x2 = -4.4375 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -4.4375 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -4.4375 + 5.0625 Combine like terms: -4.4375 + 5.0625 = 0.625 5.0625 + -4.5x + x2 = 0.625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 0.625 Calculate the square root of the right side: 0.790569415 Break this problem into two subproblems by setting (x + -2.25) equal to 0.790569415 and -0.790569415.Subproblem 1
x + -2.25 = 0.790569415 Simplifying x + -2.25 = 0.790569415 Reorder the terms: -2.25 + x = 0.790569415 Solving -2.25 + x = 0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 0.790569415 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 0.790569415 + 2.25 x = 0.790569415 + 2.25 Combine like terms: 0.790569415 + 2.25 = 3.040569415 x = 3.040569415 Simplifying x = 3.040569415Subproblem 2
x + -2.25 = -0.790569415 Simplifying x + -2.25 = -0.790569415 Reorder the terms: -2.25 + x = -0.790569415 Solving -2.25 + x = -0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -0.790569415 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -0.790569415 + 2.25 x = -0.790569415 + 2.25 Combine like terms: -0.790569415 + 2.25 = 1.459430585 x = 1.459430585 Simplifying x = 1.459430585Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.040569415, 1.459430585}
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