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Simplifying 9x + -12 = x2 + -5x Reorder the terms: -12 + 9x = x2 + -5x Reorder the terms: -12 + 9x = -5x + x2 Solving -12 + 9x = -5x + x2 Solving for variable 'x'. Combine like terms: 9x + 5x = 14x -12 + 14x + -1x2 = -5x + x2 + 5x + -1x2 Reorder the terms: -12 + 14x + -1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 -12 + 14x + -1x2 = 0 + x2 + -1x2 -12 + 14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -14x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -14x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -14x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -14x + x2 = 0 + -12 -14x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -14x + x2 = -12 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -12 + 49 Reorder the terms: 49 + -14x + x2 = -12 + 49 Combine like terms: -12 + 49 = 37 49 + -14x + x2 = 37 Factor a perfect square on the left side: (x + -7)(x + -7) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + -7) equal to 6.08276253 and -6.08276253.Subproblem 1
x + -7 = 6.08276253 Simplifying x + -7 = 6.08276253 Reorder the terms: -7 + x = 6.08276253 Solving -7 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 6.08276253 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.08276253 + 7 x = 6.08276253 + 7 Combine like terms: 6.08276253 + 7 = 13.08276253 x = 13.08276253 Simplifying x = 13.08276253Subproblem 2
x + -7 = -6.08276253 Simplifying x + -7 = -6.08276253 Reorder the terms: -7 + x = -6.08276253 Solving -7 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -6.08276253 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.08276253 + 7 x = -6.08276253 + 7 Combine like terms: -6.08276253 + 7 = 0.91723747 x = 0.91723747 Simplifying x = 0.91723747Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.08276253, 0.91723747}
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