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Simplifying 3x(x + -5) = 2x + 10 Reorder the terms: 3x(-5 + x) = 2x + 10 (-5 * 3x + x * 3x) = 2x + 10 (-15x + 3x2) = 2x + 10 Reorder the terms: -15x + 3x2 = 10 + 2x Solving -15x + 3x2 = 10 + 2x Solving for variable 'x'. Reorder the terms: -10 + -15x + -2x + 3x2 = 10 + 2x + -10 + -2x Combine like terms: -15x + -2x = -17x -10 + -17x + 3x2 = 10 + 2x + -10 + -2x Reorder the terms: -10 + -17x + 3x2 = 10 + -10 + 2x + -2x Combine like terms: 10 + -10 = 0 -10 + -17x + 3x2 = 0 + 2x + -2x -10 + -17x + 3x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -10 + -17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -5.666666667x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -5.666666667x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -5.666666667x + x2 = 0 + 3.333333333 -5.666666667x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -5.666666667x + x2 = 3.333333333 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = 3.333333333 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 3.333333333 + 8.027777782 Combine like terms: 3.333333333 + 8.027777782 = 11.361111115 8.027777782 + -5.666666667x + x2 = 11.361111115 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 11.361111115 Calculate the square root of the right side: 3.370624737 Break this problem into two subproblems by setting (x + -2.833333334) equal to 3.370624737 and -3.370624737.Subproblem 1
x + -2.833333334 = 3.370624737 Simplifying x + -2.833333334 = 3.370624737 Reorder the terms: -2.833333334 + x = 3.370624737 Solving -2.833333334 + x = 3.370624737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 3.370624737 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 3.370624737 + 2.833333334 x = 3.370624737 + 2.833333334 Combine like terms: 3.370624737 + 2.833333334 = 6.203958071 x = 6.203958071 Simplifying x = 6.203958071Subproblem 2
x + -2.833333334 = -3.370624737 Simplifying x + -2.833333334 = -3.370624737 Reorder the terms: -2.833333334 + x = -3.370624737 Solving -2.833333334 + x = -3.370624737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -3.370624737 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -3.370624737 + 2.833333334 x = -3.370624737 + 2.833333334 Combine like terms: -3.370624737 + 2.833333334 = -0.537291403 x = -0.537291403 Simplifying x = -0.537291403Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.203958071, -0.537291403}
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