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Simplifying 0 = x2 + -26x + -7 Reorder the terms: 0 = -7 + -26x + x2 Solving 0 = -7 + -26x + x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + 26x + -1x2 = -7 + -26x + x2 + 7 + 26x + -1x2 Reorder the terms: 7 + 26x + -1x2 = -7 + 7 + -26x + 26x + x2 + -1x2 Combine like terms: -7 + 7 = 0 7 + 26x + -1x2 = 0 + -26x + 26x + x2 + -1x2 7 + 26x + -1x2 = -26x + 26x + x2 + -1x2 Combine like terms: -26x + 26x = 0 7 + 26x + -1x2 = 0 + x2 + -1x2 7 + 26x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7 + 26x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -26x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -26x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -26x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -26x + x2 = 0 + 7 -26x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -26x + x2 = 7 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = 7 + 169 Reorder the terms: 169 + -26x + x2 = 7 + 169 Combine like terms: 7 + 169 = 176 169 + -26x + x2 = 176 Factor a perfect square on the left side: (x + -13)(x + -13) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (x + -13) equal to 13.266499161 and -13.266499161.Subproblem 1
x + -13 = 13.266499161 Simplifying x + -13 = 13.266499161 Reorder the terms: -13 + x = 13.266499161 Solving -13 + x = 13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 13.266499161 + 13 Combine like terms: -13 + 13 = 0 0 + x = 13.266499161 + 13 x = 13.266499161 + 13 Combine like terms: 13.266499161 + 13 = 26.266499161 x = 26.266499161 Simplifying x = 26.266499161Subproblem 2
x + -13 = -13.266499161 Simplifying x + -13 = -13.266499161 Reorder the terms: -13 + x = -13.266499161 Solving -13 + x = -13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -13.266499161 + 13 Combine like terms: -13 + 13 = 0 0 + x = -13.266499161 + 13 x = -13.266499161 + 13 Combine like terms: -13.266499161 + 13 = -0.266499161 x = -0.266499161 Simplifying x = -0.266499161Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.266499161, -0.266499161}
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