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Simplifying 12(4x + -3) = x(2x + 1) Reorder the terms: 12(-3 + 4x) = x(2x + 1) (-3 * 12 + 4x * 12) = x(2x + 1) (-36 + 48x) = x(2x + 1) Reorder the terms: -36 + 48x = x(1 + 2x) -36 + 48x = (1 * x + 2x * x) -36 + 48x = (1x + 2x2) Solving -36 + 48x = 1x + 2x2 Solving for variable 'x'. Combine like terms: 48x + -1x = 47x -36 + 47x + -2x2 = 1x + 2x2 + -1x + -2x2 Reorder the terms: -36 + 47x + -2x2 = 1x + -1x + 2x2 + -2x2 Combine like terms: 1x + -1x = 0 -36 + 47x + -2x2 = 0 + 2x2 + -2x2 -36 + 47x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -36 + 47x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 18 + -23.5x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -23.5x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -23.5x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -23.5x + x2 = 0 + -18 -23.5x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -23.5x + x2 = -18 The x term is -23.5x. Take half its coefficient (-11.75). Square it (138.0625) and add it to both sides. Add '138.0625' to each side of the equation. -23.5x + 138.0625 + x2 = -18 + 138.0625 Reorder the terms: 138.0625 + -23.5x + x2 = -18 + 138.0625 Combine like terms: -18 + 138.0625 = 120.0625 138.0625 + -23.5x + x2 = 120.0625 Factor a perfect square on the left side: (x + -11.75)(x + -11.75) = 120.0625 Calculate the square root of the right side: 10.9573035 Break this problem into two subproblems by setting (x + -11.75) equal to 10.9573035 and -10.9573035.Subproblem 1
x + -11.75 = 10.9573035 Simplifying x + -11.75 = 10.9573035 Reorder the terms: -11.75 + x = 10.9573035 Solving -11.75 + x = 10.9573035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + x = 10.9573035 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + x = 10.9573035 + 11.75 x = 10.9573035 + 11.75 Combine like terms: 10.9573035 + 11.75 = 22.7073035 x = 22.7073035 Simplifying x = 22.7073035Subproblem 2
x + -11.75 = -10.9573035 Simplifying x + -11.75 = -10.9573035 Reorder the terms: -11.75 + x = -10.9573035 Solving -11.75 + x = -10.9573035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + x = -10.9573035 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + x = -10.9573035 + 11.75 x = -10.9573035 + 11.75 Combine like terms: -10.9573035 + 11.75 = 0.7926965 x = 0.7926965 Simplifying x = 0.7926965Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.7073035, 0.7926965}
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