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Simplifying x2 + 26x + 72 = 0 Reorder the terms: 72 + 26x + x2 = 0 Solving 72 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + 26x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + 26x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + 26x + x2 = 0 + -72 26x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 26x + x2 = -72 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 = -72 + 169 Reorder the terms: 169 + 26x + x2 = -72 + 169 Combine like terms: -72 + 169 = 97 169 + 26x + x2 = 97 Factor a perfect square on the left side: (x + 13)(x + 13) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + 13) equal to 9.848857802 and -9.848857802.Subproblem 1
x + 13 = 9.848857802 Simplifying x + 13 = 9.848857802 Reorder the terms: 13 + x = 9.848857802 Solving 13 + x = 9.848857802 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 = 9.848857802 + -13 Combine like terms: 13 + -13 = 0 0 + x = 9.848857802 + -13 x = 9.848857802 + -13 Combine like terms: 9.848857802 + -13 = -3.151142198 x = -3.151142198 Simplifying x = -3.151142198Subproblem 2
x + 13 = -9.848857802 Simplifying x + 13 = -9.848857802 Reorder the terms: 13 + x = -9.848857802 Solving 13 + x = -9.848857802 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 = -9.848857802 + -13 Combine like terms: 13 + -13 = 0 0 + x = -9.848857802 + -13 x = -9.848857802 + -13 Combine like terms: -9.848857802 + -13 = -22.848857802 x = -22.848857802 Simplifying x = -22.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.151142198, -22.848857802}
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