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Simplifying (4x + -13)(2x + 35) = 180 Reorder the terms: (-13 + 4x)(2x + 35) = 180 Reorder the terms: (-13 + 4x)(35 + 2x) = 180 Multiply (-13 + 4x) * (35 + 2x) (-13(35 + 2x) + 4x * (35 + 2x)) = 180 ((35 * -13 + 2x * -13) + 4x * (35 + 2x)) = 180 ((-455 + -26x) + 4x * (35 + 2x)) = 180 (-455 + -26x + (35 * 4x + 2x * 4x)) = 180 (-455 + -26x + (140x + 8x2)) = 180 Combine like terms: -26x + 140x = 114x (-455 + 114x + 8x2) = 180 Solving -455 + 114x + 8x2 = 180 Solving for variable 'x'. Reorder the terms: -455 + -180 + 114x + 8x2 = 180 + -180 Combine like terms: -455 + -180 = -635 -635 + 114x + 8x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -635 + 114x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -79.375 + 14.25x + x2 = 0 Move the constant term to the right: Add '79.375' to each side of the equation. -79.375 + 14.25x + 79.375 + x2 = 0 + 79.375 Reorder the terms: -79.375 + 79.375 + 14.25x + x2 = 0 + 79.375 Combine like terms: -79.375 + 79.375 = 0.000 0.000 + 14.25x + x2 = 0 + 79.375 14.25x + x2 = 0 + 79.375 Combine like terms: 0 + 79.375 = 79.375 14.25x + x2 = 79.375 The x term is 14.25x. Take half its coefficient (7.125). Square it (50.765625) and add it to both sides. Add '50.765625' to each side of the equation. 14.25x + 50.765625 + x2 = 79.375 + 50.765625 Reorder the terms: 50.765625 + 14.25x + x2 = 79.375 + 50.765625 Combine like terms: 79.375 + 50.765625 = 130.140625 50.765625 + 14.25x + x2 = 130.140625 Factor a perfect square on the left side: (x + 7.125)(x + 7.125) = 130.140625 Calculate the square root of the right side: 11.407919398 Break this problem into two subproblems by setting (x + 7.125) equal to 11.407919398 and -11.407919398.Subproblem 1
x + 7.125 = 11.407919398 Simplifying x + 7.125 = 11.407919398 Reorder the terms: 7.125 + x = 11.407919398 Solving 7.125 + x = 11.407919398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.125' to each side of the equation. 7.125 + -7.125 + x = 11.407919398 + -7.125 Combine like terms: 7.125 + -7.125 = 0.000 0.000 + x = 11.407919398 + -7.125 x = 11.407919398 + -7.125 Combine like terms: 11.407919398 + -7.125 = 4.282919398 x = 4.282919398 Simplifying x = 4.282919398Subproblem 2
x + 7.125 = -11.407919398 Simplifying x + 7.125 = -11.407919398 Reorder the terms: 7.125 + x = -11.407919398 Solving 7.125 + x = -11.407919398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.125' to each side of the equation. 7.125 + -7.125 + x = -11.407919398 + -7.125 Combine like terms: 7.125 + -7.125 = 0.000 0.000 + x = -11.407919398 + -7.125 x = -11.407919398 + -7.125 Combine like terms: -11.407919398 + -7.125 = -18.532919398 x = -18.532919398 Simplifying x = -18.532919398Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.282919398, -18.532919398}
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