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Simplifying (4x + -29)(2x + -3) = x Reorder the terms: (-29 + 4x)(2x + -3) = x Reorder the terms: (-29 + 4x)(-3 + 2x) = x Multiply (-29 + 4x) * (-3 + 2x) (-29(-3 + 2x) + 4x * (-3 + 2x)) = x ((-3 * -29 + 2x * -29) + 4x * (-3 + 2x)) = x ((87 + -58x) + 4x * (-3 + 2x)) = x (87 + -58x + (-3 * 4x + 2x * 4x)) = x (87 + -58x + (-12x + 8x2)) = x Combine like terms: -58x + -12x = -70x (87 + -70x + 8x2) = x Solving 87 + -70x + 8x2 = x Solving for variable 'x'. Reorder the terms: 87 + -70x + -1x + 8x2 = x + -1x Combine like terms: -70x + -1x = -71x 87 + -71x + 8x2 = x + -1x Combine like terms: x + -1x = 0 87 + -71x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 10.875 + -8.875x + x2 = 0 Move the constant term to the right: Add '-10.875' to each side of the equation. 10.875 + -8.875x + -10.875 + x2 = 0 + -10.875 Reorder the terms: 10.875 + -10.875 + -8.875x + x2 = 0 + -10.875 Combine like terms: 10.875 + -10.875 = 0.000 0.000 + -8.875x + x2 = 0 + -10.875 -8.875x + x2 = 0 + -10.875 Combine like terms: 0 + -10.875 = -10.875 -8.875x + x2 = -10.875 The x term is -8.875x. Take half its coefficient (-4.4375). Square it (19.69140625) and add it to both sides. Add '19.69140625' to each side of the equation. -8.875x + 19.69140625 + x2 = -10.875 + 19.69140625 Reorder the terms: 19.69140625 + -8.875x + x2 = -10.875 + 19.69140625 Combine like terms: -10.875 + 19.69140625 = 8.81640625 19.69140625 + -8.875x + x2 = 8.81640625 Factor a perfect square on the left side: (x + -4.4375)(x + -4.4375) = 8.81640625 Calculate the square root of the right side: 2.96924338 Break this problem into two subproblems by setting (x + -4.4375) equal to 2.96924338 and -2.96924338.Subproblem 1
x + -4.4375 = 2.96924338 Simplifying x + -4.4375 = 2.96924338 Reorder the terms: -4.4375 + x = 2.96924338 Solving -4.4375 + x = 2.96924338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4375' to each side of the equation. -4.4375 + 4.4375 + x = 2.96924338 + 4.4375 Combine like terms: -4.4375 + 4.4375 = 0.0000 0.0000 + x = 2.96924338 + 4.4375 x = 2.96924338 + 4.4375 Combine like terms: 2.96924338 + 4.4375 = 7.40674338 x = 7.40674338 Simplifying x = 7.40674338Subproblem 2
x + -4.4375 = -2.96924338 Simplifying x + -4.4375 = -2.96924338 Reorder the terms: -4.4375 + x = -2.96924338 Solving -4.4375 + x = -2.96924338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4375' to each side of the equation. -4.4375 + 4.4375 + x = -2.96924338 + 4.4375 Combine like terms: -4.4375 + 4.4375 = 0.0000 0.0000 + x = -2.96924338 + 4.4375 x = -2.96924338 + 4.4375 Combine like terms: -2.96924338 + 4.4375 = 1.46825662 x = 1.46825662 Simplifying x = 1.46825662Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.40674338, 1.46825662}
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