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Simplifying 13x + -12 = 2x2 Reorder the terms: -12 + 13x = 2x2 Solving -12 + 13x = 2x2 Solving for variable 'x'. Combine like terms: 2x2 + -2x2 = 0 -12 + 13x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 6 + -6.5x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -6.5x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -6.5x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -6.5x + x2 = 0 + -6 -6.5x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -6.5x + x2 = -6 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = -6 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -6 + 10.5625 Combine like terms: -6 + 10.5625 = 4.5625 10.5625 + -6.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + -3.25) equal to 2.136000936 and -2.136000936.Subproblem 1
x + -3.25 = 2.136000936 Simplifying x + -3.25 = 2.136000936 Reorder the terms: -3.25 + x = 2.136000936 Solving -3.25 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 2.136000936 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 2.136000936 + 3.25 x = 2.136000936 + 3.25 Combine like terms: 2.136000936 + 3.25 = 5.386000936 x = 5.386000936 Simplifying x = 5.386000936Subproblem 2
x + -3.25 = -2.136000936 Simplifying x + -3.25 = -2.136000936 Reorder the terms: -3.25 + x = -2.136000936 Solving -3.25 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -2.136000936 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -2.136000936 + 3.25 x = -2.136000936 + 3.25 Combine like terms: -2.136000936 + 3.25 = 1.113999064 x = 1.113999064 Simplifying x = 1.113999064Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.386000936, 1.113999064}
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