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Simplifying (2x + -2)(3x + 10) = x Reorder the terms: (-2 + 2x)(3x + 10) = x Reorder the terms: (-2 + 2x)(10 + 3x) = x Multiply (-2 + 2x) * (10 + 3x) (-2(10 + 3x) + 2x * (10 + 3x)) = x ((10 * -2 + 3x * -2) + 2x * (10 + 3x)) = x ((-20 + -6x) + 2x * (10 + 3x)) = x (-20 + -6x + (10 * 2x + 3x * 2x)) = x (-20 + -6x + (20x + 6x2)) = x Combine like terms: -6x + 20x = 14x (-20 + 14x + 6x2) = x Solving -20 + 14x + 6x2 = x Solving for variable 'x'. Reorder the terms: -20 + 14x + -1x + 6x2 = x + -1x Combine like terms: 14x + -1x = 13x -20 + 13x + 6x2 = x + -1x Combine like terms: x + -1x = 0 -20 + 13x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.333333333 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 2.166666667x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 2.166666667x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 2.166666667x + x2 = 0 + 3.333333333 2.166666667x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 2.166666667x + x2 = 3.333333333 The x term is 2.166666667x. Take half its coefficient (1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. 2.166666667x + 1.173611113 + x2 = 3.333333333 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = 3.333333333 + 1.173611113 Combine like terms: 3.333333333 + 1.173611113 = 4.506944446 1.173611113 + 2.166666667x + x2 = 4.506944446 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = 4.506944446 Calculate the square root of the right side: 2.122956534 Break this problem into two subproblems by setting (x + 1.083333334) equal to 2.122956534 and -2.122956534.Subproblem 1
x + 1.083333334 = 2.122956534 Simplifying x + 1.083333334 = 2.122956534 Reorder the terms: 1.083333334 + x = 2.122956534 Solving 1.083333334 + x = 2.122956534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = 2.122956534 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 2.122956534 + -1.083333334 x = 2.122956534 + -1.083333334 Combine like terms: 2.122956534 + -1.083333334 = 1.0396232 x = 1.0396232 Simplifying x = 1.0396232Subproblem 2
x + 1.083333334 = -2.122956534 Simplifying x + 1.083333334 = -2.122956534 Reorder the terms: 1.083333334 + x = -2.122956534 Solving 1.083333334 + x = -2.122956534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = -2.122956534 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -2.122956534 + -1.083333334 x = -2.122956534 + -1.083333334 Combine like terms: -2.122956534 + -1.083333334 = -3.206289868 x = -3.206289868 Simplifying x = -3.206289868Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0396232, -3.206289868}
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