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Simplifying (2x + -1)(x + -13) = 70 Reorder the terms: (-1 + 2x)(x + -13) = 70 Reorder the terms: (-1 + 2x)(-13 + x) = 70 Multiply (-1 + 2x) * (-13 + x) (-1(-13 + x) + 2x * (-13 + x)) = 70 ((-13 * -1 + x * -1) + 2x * (-13 + x)) = 70 ((13 + -1x) + 2x * (-13 + x)) = 70 (13 + -1x + (-13 * 2x + x * 2x)) = 70 (13 + -1x + (-26x + 2x2)) = 70 Combine like terms: -1x + -26x = -27x (13 + -27x + 2x2) = 70 Solving 13 + -27x + 2x2 = 70 Solving for variable 'x'. Reorder the terms: 13 + -70 + -27x + 2x2 = 70 + -70 Combine like terms: 13 + -70 = -57 -57 + -27x + 2x2 = 70 + -70 Combine like terms: 70 + -70 = 0 -57 + -27x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -28.5 + -13.5x + x2 = 0 Move the constant term to the right: Add '28.5' to each side of the equation. -28.5 + -13.5x + 28.5 + x2 = 0 + 28.5 Reorder the terms: -28.5 + 28.5 + -13.5x + x2 = 0 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + -13.5x + x2 = 0 + 28.5 -13.5x + x2 = 0 + 28.5 Combine like terms: 0 + 28.5 = 28.5 -13.5x + x2 = 28.5 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = 28.5 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = 28.5 + 45.5625 Combine like terms: 28.5 + 45.5625 = 74.0625 45.5625 + -13.5x + x2 = 74.0625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 74.0625 Calculate the square root of the right side: 8.605957239 Break this problem into two subproblems by setting (x + -6.75) equal to 8.605957239 and -8.605957239.Subproblem 1
x + -6.75 = 8.605957239 Simplifying x + -6.75 = 8.605957239 Reorder the terms: -6.75 + x = 8.605957239 Solving -6.75 + x = 8.605957239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 8.605957239 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 8.605957239 + 6.75 x = 8.605957239 + 6.75 Combine like terms: 8.605957239 + 6.75 = 15.355957239 x = 15.355957239 Simplifying x = 15.355957239Subproblem 2
x + -6.75 = -8.605957239 Simplifying x + -6.75 = -8.605957239 Reorder the terms: -6.75 + x = -8.605957239 Solving -6.75 + x = -8.605957239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -8.605957239 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -8.605957239 + 6.75 x = -8.605957239 + 6.75 Combine like terms: -8.605957239 + 6.75 = -1.855957239 x = -1.855957239 Simplifying x = -1.855957239Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.355957239, -1.855957239}
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