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Simplifying (2x + 5)(x + -9) = 14 Reorder the terms: (5 + 2x)(x + -9) = 14 Reorder the terms: (5 + 2x)(-9 + x) = 14 Multiply (5 + 2x) * (-9 + x) (5(-9 + x) + 2x * (-9 + x)) = 14 ((-9 * 5 + x * 5) + 2x * (-9 + x)) = 14 ((-45 + 5x) + 2x * (-9 + x)) = 14 (-45 + 5x + (-9 * 2x + x * 2x)) = 14 (-45 + 5x + (-18x + 2x2)) = 14 Combine like terms: 5x + -18x = -13x (-45 + -13x + 2x2) = 14 Solving -45 + -13x + 2x2 = 14 Solving for variable 'x'. Reorder the terms: -45 + -14 + -13x + 2x2 = 14 + -14 Combine like terms: -45 + -14 = -59 -59 + -13x + 2x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -59 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -29.5 + -6.5x + x2 = 0 Move the constant term to the right: Add '29.5' to each side of the equation. -29.5 + -6.5x + 29.5 + x2 = 0 + 29.5 Reorder the terms: -29.5 + 29.5 + -6.5x + x2 = 0 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + -6.5x + x2 = 0 + 29.5 -6.5x + x2 = 0 + 29.5 Combine like terms: 0 + 29.5 = 29.5 -6.5x + x2 = 29.5 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 29.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 29.5 + 10.5625 Combine like terms: 29.5 + 10.5625 = 40.0625 10.5625 + -6.5x + x2 = 40.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 40.0625 Calculate the square root of the right side: 6.329494451 Break this problem into two subproblems by setting (x + -3.25) equal to 6.329494451 and -6.329494451.Subproblem 1
x + -3.25 = 6.329494451 Simplifying x + -3.25 = 6.329494451 Reorder the terms: -3.25 + x = 6.329494451 Solving -3.25 + x = 6.329494451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 6.329494451 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 6.329494451 + 3.25 x = 6.329494451 + 3.25 Combine like terms: 6.329494451 + 3.25 = 9.579494451 x = 9.579494451 Simplifying x = 9.579494451Subproblem 2
x + -3.25 = -6.329494451 Simplifying x + -3.25 = -6.329494451 Reorder the terms: -3.25 + x = -6.329494451 Solving -3.25 + x = -6.329494451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -6.329494451 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -6.329494451 + 3.25 x = -6.329494451 + 3.25 Combine like terms: -6.329494451 + 3.25 = -3.079494451 x = -3.079494451 Simplifying x = -3.079494451Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.579494451, -3.079494451}
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