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Simplifying x2 + 26x = -145 Reorder the terms: 26x + x2 = -145 Solving 26x + x2 = -145 Solving for variable 'x'. Reorder the terms: 145 + 26x + x2 = -145 + 145 Combine like terms: -145 + 145 = 0 145 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-145' to each side of the equation. 145 + 26x + -145 + x2 = 0 + -145 Reorder the terms: 145 + -145 + 26x + x2 = 0 + -145 Combine like terms: 145 + -145 = 0 0 + 26x + x2 = 0 + -145 26x + x2 = 0 + -145 Combine like terms: 0 + -145 = -145 26x + x2 = -145 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 = -145 + 169 Reorder the terms: 169 + 26x + x2 = -145 + 169 Combine like terms: -145 + 169 = 24 169 + 26x + x2 = 24 Factor a perfect square on the left side: (x + 13)(x + 13) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + 13) equal to 4.898979486 and -4.898979486.Subproblem 1
x + 13 = 4.898979486 Simplifying x + 13 = 4.898979486 Reorder the terms: 13 + x = 4.898979486 Solving 13 + x = 4.898979486 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 = 4.898979486 + -13 Combine like terms: 13 + -13 = 0 0 + x = 4.898979486 + -13 x = 4.898979486 + -13 Combine like terms: 4.898979486 + -13 = -8.101020514 x = -8.101020514 Simplifying x = -8.101020514Subproblem 2
x + 13 = -4.898979486 Simplifying x + 13 = -4.898979486 Reorder the terms: 13 + x = -4.898979486 Solving 13 + x = -4.898979486 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 = -4.898979486 + -13 Combine like terms: 13 + -13 = 0 0 + x = -4.898979486 + -13 x = -4.898979486 + -13 Combine like terms: -4.898979486 + -13 = -17.898979486 x = -17.898979486 Simplifying x = -17.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.101020514, -17.898979486}
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