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Simplifying 9x + -2x(x + 10) = 6(x + -5) + 3x Reorder the terms: 9x + -2x(10 + x) = 6(x + -5) + 3x 9x + (10 * -2x + x * -2x) = 6(x + -5) + 3x 9x + (-20x + -2x2) = 6(x + -5) + 3x Combine like terms: 9x + -20x = -11x -11x + -2x2 = 6(x + -5) + 3x Reorder the terms: -11x + -2x2 = 6(-5 + x) + 3x -11x + -2x2 = (-5 * 6 + x * 6) + 3x -11x + -2x2 = (-30 + 6x) + 3x Combine like terms: 6x + 3x = 9x -11x + -2x2 = -30 + 9x Solving -11x + -2x2 = -30 + 9x Solving for variable 'x'. Reorder the terms: 30 + -11x + -9x + -2x2 = -30 + 9x + 30 + -9x Combine like terms: -11x + -9x = -20x 30 + -20x + -2x2 = -30 + 9x + 30 + -9x Reorder the terms: 30 + -20x + -2x2 = -30 + 30 + 9x + -9x Combine like terms: -30 + 30 = 0 30 + -20x + -2x2 = 0 + 9x + -9x 30 + -20x + -2x2 = 9x + -9x Combine like terms: 9x + -9x = 0 30 + -20x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -10x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -10x + -1x2)' equal to zero and attempt to solve: Simplifying 15 + -10x + -1x2 = 0 Solving 15 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + 10x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 10x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 10x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 10x + x2 = 0 + 15 10x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 10x + x2 = 15 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 15 + 25 Reorder the terms: 25 + 10x + x2 = 15 + 25 Combine like terms: 15 + 25 = 40 25 + 10x + x2 = 40 Factor a perfect square on the left side: (x + 5)(x + 5) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + 5) equal to 6.32455532 and -6.32455532.Subproblem 1
x + 5 = 6.32455532 Simplifying x + 5 = 6.32455532 Reorder the terms: 5 + x = 6.32455532 Solving 5 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 6.32455532 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.32455532 + -5 x = 6.32455532 + -5 Combine like terms: 6.32455532 + -5 = 1.32455532 x = 1.32455532 Simplifying x = 1.32455532Subproblem 2
x + 5 = -6.32455532 Simplifying x + 5 = -6.32455532 Reorder the terms: 5 + x = -6.32455532 Solving 5 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -6.32455532 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.32455532 + -5 x = -6.32455532 + -5 Combine like terms: -6.32455532 + -5 = -11.32455532 x = -11.32455532 Simplifying x = -11.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.32455532, -11.32455532}Solution
x = {1.32455532, -11.32455532}
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