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Simplifying 56x = 50x2 + 20x + -6 Reorder the terms: 56x = -6 + 20x + 50x2 Solving 56x = -6 + 20x + 50x2 Solving for variable 'x'. Reorder the terms: 6 + 56x + -20x + -50x2 = -6 + 20x + 50x2 + 6 + -20x + -50x2 Combine like terms: 56x + -20x = 36x 6 + 36x + -50x2 = -6 + 20x + 50x2 + 6 + -20x + -50x2 Reorder the terms: 6 + 36x + -50x2 = -6 + 6 + 20x + -20x + 50x2 + -50x2 Combine like terms: -6 + 6 = 0 6 + 36x + -50x2 = 0 + 20x + -20x + 50x2 + -50x2 6 + 36x + -50x2 = 20x + -20x + 50x2 + -50x2 Combine like terms: 20x + -20x = 0 6 + 36x + -50x2 = 0 + 50x2 + -50x2 6 + 36x + -50x2 = 50x2 + -50x2 Combine like terms: 50x2 + -50x2 = 0 6 + 36x + -50x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 18x + -25x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 18x + -25x2)' equal to zero and attempt to solve: Simplifying 3 + 18x + -25x2 = 0 Solving 3 + 18x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.12 + -0.72x + x2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + -0.72x + 0.12 + x2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + -0.72x + x2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + -0.72x + x2 = 0 + 0.12 -0.72x + x2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 -0.72x + x2 = 0.12 The x term is -0.72x. Take half its coefficient (-0.36). Square it (0.1296) and add it to both sides. Add '0.1296' to each side of the equation. -0.72x + 0.1296 + x2 = 0.12 + 0.1296 Reorder the terms: 0.1296 + -0.72x + x2 = 0.12 + 0.1296 Combine like terms: 0.12 + 0.1296 = 0.2496 0.1296 + -0.72x + x2 = 0.2496 Factor a perfect square on the left side: (x + -0.36)(x + -0.36) = 0.2496 Calculate the square root of the right side: 0.49959984 Break this problem into two subproblems by setting (x + -0.36) equal to 0.49959984 and -0.49959984.Subproblem 1
x + -0.36 = 0.49959984 Simplifying x + -0.36 = 0.49959984 Reorder the terms: -0.36 + x = 0.49959984 Solving -0.36 + x = 0.49959984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.36' to each side of the equation. -0.36 + 0.36 + x = 0.49959984 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + x = 0.49959984 + 0.36 x = 0.49959984 + 0.36 Combine like terms: 0.49959984 + 0.36 = 0.85959984 x = 0.85959984 Simplifying x = 0.85959984Subproblem 2
x + -0.36 = -0.49959984 Simplifying x + -0.36 = -0.49959984 Reorder the terms: -0.36 + x = -0.49959984 Solving -0.36 + x = -0.49959984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.36' to each side of the equation. -0.36 + 0.36 + x = -0.49959984 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + x = -0.49959984 + 0.36 x = -0.49959984 + 0.36 Combine like terms: -0.49959984 + 0.36 = -0.13959984 x = -0.13959984 Simplifying x = -0.13959984Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.85959984, -0.13959984}Solution
x = {0.85959984, -0.13959984}
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