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Simplifying x2 + -12x = 14 Reorder the terms: -12x + x2 = 14 Solving -12x + x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + -12x + x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -12x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -12x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -12x + x2 = 0 + 14 -12x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -12x + x2 = 14 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 14 + 36 Reorder the terms: 36 + -12x + x2 = 14 + 36 Combine like terms: 14 + 36 = 50 36 + -12x + x2 = 50 Factor a perfect square on the left side: (x + -6)(x + -6) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + -6) equal to 7.071067812 and -7.071067812.Subproblem 1
x + -6 = 7.071067812 Simplifying x + -6 = 7.071067812 Reorder the terms: -6 + x = 7.071067812 Solving -6 + x = 7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.071067812 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.071067812 + 6 x = 7.071067812 + 6 Combine like terms: 7.071067812 + 6 = 13.071067812 x = 13.071067812 Simplifying x = 13.071067812Subproblem 2
x + -6 = -7.071067812 Simplifying x + -6 = -7.071067812 Reorder the terms: -6 + x = -7.071067812 Solving -6 + x = -7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.071067812 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.071067812 + 6 x = -7.071067812 + 6 Combine like terms: -7.071067812 + 6 = -1.071067812 x = -1.071067812 Simplifying x = -1.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.071067812, -1.071067812}
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