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Simplifying 0 = x2 + -14x + -14 Reorder the terms: 0 = -14 + -14x + x2 Solving 0 = -14 + -14x + x2 Solving for variable 'x'. Combine like terms: 0 + 14 = 14 14 + 14x + -1x2 = -14 + -14x + x2 + 14 + 14x + -1x2 Reorder the terms: 14 + 14x + -1x2 = -14 + 14 + -14x + 14x + x2 + -1x2 Combine like terms: -14 + 14 = 0 14 + 14x + -1x2 = 0 + -14x + 14x + x2 + -1x2 14 + 14x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 14 + 14x + -1x2 = 0 + x2 + -1x2 14 + 14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 14 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + -14x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -14x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -14x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -14x + x2 = 0 + 14 -14x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -14x + x2 = 14 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 = 14 + 49 Reorder the terms: 49 + -14x + x2 = 14 + 49 Combine like terms: 14 + 49 = 63 49 + -14x + x2 = 63 Factor a perfect square on the left side: (x + -7)(x + -7) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + -7) equal to 7.937253933 and -7.937253933.Subproblem 1
x + -7 = 7.937253933 Simplifying x + -7 = 7.937253933 Reorder the terms: -7 + x = 7.937253933 Solving -7 + x = 7.937253933 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 = 7.937253933 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.937253933 + 7 x = 7.937253933 + 7 Combine like terms: 7.937253933 + 7 = 14.937253933 x = 14.937253933 Simplifying x = 14.937253933Subproblem 2
x + -7 = -7.937253933 Simplifying x + -7 = -7.937253933 Reorder the terms: -7 + x = -7.937253933 Solving -7 + x = -7.937253933 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 = -7.937253933 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.937253933 + 7 x = -7.937253933 + 7 Combine like terms: -7.937253933 + 7 = -0.937253933 x = -0.937253933 Simplifying x = -0.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.937253933, -0.937253933}
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