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Simplifying 9(13 + -1x) + -4x = 5(21 + -2x) * 9x (13 * 9 + -1x * 9) + -4x = 5(21 + -2x) * 9x (117 + -9x) + -4x = 5(21 + -2x) * 9x Combine like terms: -9x + -4x = -13x 117 + -13x = 5(21 + -2x) * 9x Reorder the terms for easier multiplication: 117 + -13x = 5 * 9x(21 + -2x) Multiply 5 * 9 117 + -13x = 45x(21 + -2x) 117 + -13x = (21 * 45x + -2x * 45x) 117 + -13x = (945x + -90x2) Solving 117 + -13x = 945x + -90x2 Solving for variable 'x'. Combine like terms: -13x + -945x = -958x 117 + -958x + 90x2 = 945x + -90x2 + -945x + 90x2 Reorder the terms: 117 + -958x + 90x2 = 945x + -945x + -90x2 + 90x2 Combine like terms: 945x + -945x = 0 117 + -958x + 90x2 = 0 + -90x2 + 90x2 117 + -958x + 90x2 = -90x2 + 90x2 Combine like terms: -90x2 + 90x2 = 0 117 + -958x + 90x2 = 0 Begin completing the square. Divide all terms by 90 the coefficient of the squared term: Divide each side by '90'. 1.3 + -10.64444444x + x2 = 0 Move the constant term to the right: Add '-1.3' to each side of the equation. 1.3 + -10.64444444x + -1.3 + x2 = 0 + -1.3 Reorder the terms: 1.3 + -1.3 + -10.64444444x + x2 = 0 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + -10.64444444x + x2 = 0 + -1.3 -10.64444444x + x2 = 0 + -1.3 Combine like terms: 0 + -1.3 = -1.3 -10.64444444x + x2 = -1.3 The x term is -10.64444444x. Take half its coefficient (-5.32222222). Square it (28.32604936) and add it to both sides. Add '28.32604936' to each side of the equation. -10.64444444x + 28.32604936 + x2 = -1.3 + 28.32604936 Reorder the terms: 28.32604936 + -10.64444444x + x2 = -1.3 + 28.32604936 Combine like terms: -1.3 + 28.32604936 = 27.02604936 28.32604936 + -10.64444444x + x2 = 27.02604936 Factor a perfect square on the left side: (x + -5.32222222)(x + -5.32222222) = 27.02604936 Calculate the square root of the right side: 5.198658419 Break this problem into two subproblems by setting (x + -5.32222222) equal to 5.198658419 and -5.198658419.Subproblem 1
x + -5.32222222 = 5.198658419 Simplifying x + -5.32222222 = 5.198658419 Reorder the terms: -5.32222222 + x = 5.198658419 Solving -5.32222222 + x = 5.198658419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.32222222' to each side of the equation. -5.32222222 + 5.32222222 + x = 5.198658419 + 5.32222222 Combine like terms: -5.32222222 + 5.32222222 = 0.00000000 0.00000000 + x = 5.198658419 + 5.32222222 x = 5.198658419 + 5.32222222 Combine like terms: 5.198658419 + 5.32222222 = 10.520880639 x = 10.520880639 Simplifying x = 10.520880639Subproblem 2
x + -5.32222222 = -5.198658419 Simplifying x + -5.32222222 = -5.198658419 Reorder the terms: -5.32222222 + x = -5.198658419 Solving -5.32222222 + x = -5.198658419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.32222222' to each side of the equation. -5.32222222 + 5.32222222 + x = -5.198658419 + 5.32222222 Combine like terms: -5.32222222 + 5.32222222 = 0.00000000 0.00000000 + x = -5.198658419 + 5.32222222 x = -5.198658419 + 5.32222222 Combine like terms: -5.198658419 + 5.32222222 = 0.123563801 x = 0.123563801 Simplifying x = 0.123563801Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.520880639, 0.123563801}
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