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Simplifying 4x + -8 = x2 + -14x + 14 Reorder the terms: -8 + 4x = x2 + -14x + 14 Reorder the terms: -8 + 4x = 14 + -14x + x2 Solving -8 + 4x = 14 + -14x + x2 Solving for variable 'x'. Reorder the terms: -8 + -14 + 4x + 14x + -1x2 = 14 + -14x + x2 + -14 + 14x + -1x2 Combine like terms: -8 + -14 = -22 -22 + 4x + 14x + -1x2 = 14 + -14x + x2 + -14 + 14x + -1x2 Combine like terms: 4x + 14x = 18x -22 + 18x + -1x2 = 14 + -14x + x2 + -14 + 14x + -1x2 Reorder the terms: -22 + 18x + -1x2 = 14 + -14 + -14x + 14x + x2 + -1x2 Combine like terms: 14 + -14 = 0 -22 + 18x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -22 + 18x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -22 + 18x + -1x2 = 0 + x2 + -1x2 -22 + 18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -22 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 22 + -18x + x2 = 0 Move the constant term to the right: Add '-22' to each side of the equation. 22 + -18x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + -18x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -18x + x2 = 0 + -22 -18x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 -18x + x2 = -22 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -22 + 81 Reorder the terms: 81 + -18x + x2 = -22 + 81 Combine like terms: -22 + 81 = 59 81 + -18x + x2 = 59 Factor a perfect square on the left side: (x + -9)(x + -9) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + -9) equal to 7.681145748 and -7.681145748.Subproblem 1
x + -9 = 7.681145748 Simplifying x + -9 = 7.681145748 Reorder the terms: -9 + x = 7.681145748 Solving -9 + x = 7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 7.681145748 + 9 Combine like terms: -9 + 9 = 0 0 + x = 7.681145748 + 9 x = 7.681145748 + 9 Combine like terms: 7.681145748 + 9 = 16.681145748 x = 16.681145748 Simplifying x = 16.681145748Subproblem 2
x + -9 = -7.681145748 Simplifying x + -9 = -7.681145748 Reorder the terms: -9 + x = -7.681145748 Solving -9 + x = -7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -7.681145748 + 9 Combine like terms: -9 + 9 = 0 0 + x = -7.681145748 + 9 x = -7.681145748 + 9 Combine like terms: -7.681145748 + 9 = 1.318854252 x = 1.318854252 Simplifying x = 1.318854252Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.681145748, 1.318854252}
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