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Simplifying x2 = -14x + -12 Reorder the terms: x2 = -12 + -14x Solving x2 = -12 + -14x Solving for variable 'x'. Reorder the terms: 12 + 14x + x2 = -12 + -14x + 12 + 14x Reorder the terms: 12 + 14x + x2 = -12 + 12 + -14x + 14x Combine like terms: -12 + 12 = 0 12 + 14x + x2 = 0 + -14x + 14x 12 + 14x + x2 = -14x + 14x Combine like terms: -14x + 14x = 0 12 + 14x + x2 = 0 Begin completing the square. 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 = -0.91723747 x = -0.91723747 Simplifying x = -0.91723747Subproblem 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 = -13.08276253 x = -13.08276253 Simplifying x = -13.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.91723747, -13.08276253}
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