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Simplifying 5x(20 + 13x) = 12 (20 * 5x + 13x * 5x) = 12 (100x + 65x2) = 12 Solving 100x + 65x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 100x + 65x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 100x + 65x2 = 0 Begin completing the square. Divide all terms by 65 the coefficient of the squared term: Divide each side by '65'. -0.1846153846 + 1.538461538x + x2 = 0 Move the constant term to the right: Add '0.1846153846' to each side of the equation. -0.1846153846 + 1.538461538x + 0.1846153846 + x2 = 0 + 0.1846153846 Reorder the terms: -0.1846153846 + 0.1846153846 + 1.538461538x + x2 = 0 + 0.1846153846 Combine like terms: -0.1846153846 + 0.1846153846 = 0.0000000000 0.0000000000 + 1.538461538x + x2 = 0 + 0.1846153846 1.538461538x + x2 = 0 + 0.1846153846 Combine like terms: 0 + 0.1846153846 = 0.1846153846 1.538461538x + x2 = 0.1846153846 The x term is 1.538461538x. Take half its coefficient (0.769230769). Square it (0.5917159760) and add it to both sides. Add '0.5917159760' to each side of the equation. 1.538461538x + 0.5917159760 + x2 = 0.1846153846 + 0.5917159760 Reorder the terms: 0.5917159760 + 1.538461538x + x2 = 0.1846153846 + 0.5917159760 Combine like terms: 0.1846153846 + 0.5917159760 = 0.7763313606 0.5917159760 + 1.538461538x + x2 = 0.7763313606 Factor a perfect square on the left side: (x + 0.769230769)(x + 0.769230769) = 0.7763313606 Calculate the square root of the right side: 0.881096681 Break this problem into two subproblems by setting (x + 0.769230769) equal to 0.881096681 and -0.881096681.Subproblem 1
x + 0.769230769 = 0.881096681 Simplifying x + 0.769230769 = 0.881096681 Reorder the terms: 0.769230769 + x = 0.881096681 Solving 0.769230769 + x = 0.881096681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.769230769' to each side of the equation. 0.769230769 + -0.769230769 + x = 0.881096681 + -0.769230769 Combine like terms: 0.769230769 + -0.769230769 = 0.000000000 0.000000000 + x = 0.881096681 + -0.769230769 x = 0.881096681 + -0.769230769 Combine like terms: 0.881096681 + -0.769230769 = 0.111865912 x = 0.111865912 Simplifying x = 0.111865912Subproblem 2
x + 0.769230769 = -0.881096681 Simplifying x + 0.769230769 = -0.881096681 Reorder the terms: 0.769230769 + x = -0.881096681 Solving 0.769230769 + x = -0.881096681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.769230769' to each side of the equation. 0.769230769 + -0.769230769 + x = -0.881096681 + -0.769230769 Combine like terms: 0.769230769 + -0.769230769 = 0.000000000 0.000000000 + x = -0.881096681 + -0.769230769 x = -0.881096681 + -0.769230769 Combine like terms: -0.881096681 + -0.769230769 = -1.65032745 x = -1.65032745 Simplifying x = -1.65032745Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.111865912, -1.65032745}
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