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Simplifying 111 = x2 + 26x Reorder the terms: 111 = 26x + x2 Solving 111 = 26x + x2 Solving for variable 'x'. Reorder the terms: 111 + -26x + -1x2 = 26x + -26x + x2 + -1x2 Combine like terms: 26x + -26x = 0 111 + -26x + -1x2 = 0 + x2 + -1x2 111 + -26x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 111 + -26x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -111 + 26x + x2 = 0 Move the constant term to the right: Add '111' to each side of the equation. -111 + 26x + 111 + x2 = 0 + 111 Reorder the terms: -111 + 111 + 26x + x2 = 0 + 111 Combine like terms: -111 + 111 = 0 0 + 26x + x2 = 0 + 111 26x + x2 = 0 + 111 Combine like terms: 0 + 111 = 111 26x + x2 = 111 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 = 111 + 169 Reorder the terms: 169 + 26x + x2 = 111 + 169 Combine like terms: 111 + 169 = 280 169 + 26x + x2 = 280 Factor a perfect square on the left side: (x + 13)(x + 13) = 280 Calculate the square root of the right side: 16.733200531 Break this problem into two subproblems by setting (x + 13) equal to 16.733200531 and -16.733200531.Subproblem 1
x + 13 = 16.733200531 Simplifying x + 13 = 16.733200531 Reorder the terms: 13 + x = 16.733200531 Solving 13 + x = 16.733200531 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 = 16.733200531 + -13 Combine like terms: 13 + -13 = 0 0 + x = 16.733200531 + -13 x = 16.733200531 + -13 Combine like terms: 16.733200531 + -13 = 3.733200531 x = 3.733200531 Simplifying x = 3.733200531Subproblem 2
x + 13 = -16.733200531 Simplifying x + 13 = -16.733200531 Reorder the terms: 13 + x = -16.733200531 Solving 13 + x = -16.733200531 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 = -16.733200531 + -13 Combine like terms: 13 + -13 = 0 0 + x = -16.733200531 + -13 x = -16.733200531 + -13 Combine like terms: -16.733200531 + -13 = -29.733200531 x = -29.733200531 Simplifying x = -29.733200531Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.733200531, -29.733200531}
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