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Simplifying -10 + -5x + -14 = 2x(9 + -1x) Reorder the terms: -10 + -14 + -5x = 2x(9 + -1x) Combine like terms: -10 + -14 = -24 -24 + -5x = 2x(9 + -1x) -24 + -5x = (9 * 2x + -1x * 2x) -24 + -5x = (18x + -2x2) Solving -24 + -5x = 18x + -2x2 Solving for variable 'x'. Combine like terms: -5x + -18x = -23x -24 + -23x + 2x2 = 18x + -2x2 + -18x + 2x2 Reorder the terms: -24 + -23x + 2x2 = 18x + -18x + -2x2 + 2x2 Combine like terms: 18x + -18x = 0 -24 + -23x + 2x2 = 0 + -2x2 + 2x2 -24 + -23x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -24 + -23x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12 + -11.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -11.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -11.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -11.5x + x2 = 0 + 12 -11.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -11.5x + x2 = 12 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = 12 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = 12 + 33.0625 Combine like terms: 12 + 33.0625 = 45.0625 33.0625 + -11.5x + x2 = 45.0625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 45.0625 Calculate the square root of the right side: 6.712860791 Break this problem into two subproblems by setting (x + -5.75) equal to 6.712860791 and -6.712860791.Subproblem 1
x + -5.75 = 6.712860791 Simplifying x + -5.75 = 6.712860791 Reorder the terms: -5.75 + x = 6.712860791 Solving -5.75 + x = 6.712860791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 6.712860791 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 6.712860791 + 5.75 x = 6.712860791 + 5.75 Combine like terms: 6.712860791 + 5.75 = 12.462860791 x = 12.462860791 Simplifying x = 12.462860791Subproblem 2
x + -5.75 = -6.712860791 Simplifying x + -5.75 = -6.712860791 Reorder the terms: -5.75 + x = -6.712860791 Solving -5.75 + x = -6.712860791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -6.712860791 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -6.712860791 + 5.75 x = -6.712860791 + 5.75 Combine like terms: -6.712860791 + 5.75 = -0.962860791 x = -0.962860791 Simplifying x = -0.962860791Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.462860791, -0.962860791}
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