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Simplifying (4x + -101)(2x + 3) = 180 Reorder the terms: (-101 + 4x)(2x + 3) = 180 Reorder the terms: (-101 + 4x)(3 + 2x) = 180 Multiply (-101 + 4x) * (3 + 2x) (-101(3 + 2x) + 4x * (3 + 2x)) = 180 ((3 * -101 + 2x * -101) + 4x * (3 + 2x)) = 180 ((-303 + -202x) + 4x * (3 + 2x)) = 180 (-303 + -202x + (3 * 4x + 2x * 4x)) = 180 (-303 + -202x + (12x + 8x2)) = 180 Combine like terms: -202x + 12x = -190x (-303 + -190x + 8x2) = 180 Solving -303 + -190x + 8x2 = 180 Solving for variable 'x'. Reorder the terms: -303 + -180 + -190x + 8x2 = 180 + -180 Combine like terms: -303 + -180 = -483 -483 + -190x + 8x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -483 + -190x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -60.375 + -23.75x + x2 = 0 Move the constant term to the right: Add '60.375' to each side of the equation. -60.375 + -23.75x + 60.375 + x2 = 0 + 60.375 Reorder the terms: -60.375 + 60.375 + -23.75x + x2 = 0 + 60.375 Combine like terms: -60.375 + 60.375 = 0.000 0.000 + -23.75x + x2 = 0 + 60.375 -23.75x + x2 = 0 + 60.375 Combine like terms: 0 + 60.375 = 60.375 -23.75x + x2 = 60.375 The x term is -23.75x. Take half its coefficient (-11.875). Square it (141.015625) and add it to both sides. Add '141.015625' to each side of the equation. -23.75x + 141.015625 + x2 = 60.375 + 141.015625 Reorder the terms: 141.015625 + -23.75x + x2 = 60.375 + 141.015625 Combine like terms: 60.375 + 141.015625 = 201.390625 141.015625 + -23.75x + x2 = 201.390625 Factor a perfect square on the left side: (x + -11.875)(x + -11.875) = 201.390625 Calculate the square root of the right side: 14.191216474 Break this problem into two subproblems by setting (x + -11.875) equal to 14.191216474 and -14.191216474.Subproblem 1
x + -11.875 = 14.191216474 Simplifying x + -11.875 = 14.191216474 Reorder the terms: -11.875 + x = 14.191216474 Solving -11.875 + x = 14.191216474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.875' to each side of the equation. -11.875 + 11.875 + x = 14.191216474 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + x = 14.191216474 + 11.875 x = 14.191216474 + 11.875 Combine like terms: 14.191216474 + 11.875 = 26.066216474 x = 26.066216474 Simplifying x = 26.066216474Subproblem 2
x + -11.875 = -14.191216474 Simplifying x + -11.875 = -14.191216474 Reorder the terms: -11.875 + x = -14.191216474 Solving -11.875 + x = -14.191216474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.875' to each side of the equation. -11.875 + 11.875 + x = -14.191216474 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + x = -14.191216474 + 11.875 x = -14.191216474 + 11.875 Combine like terms: -14.191216474 + 11.875 = -2.316216474 x = -2.316216474 Simplifying x = -2.316216474Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.066216474, -2.316216474}
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