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Simplifying x2 + -26x + 114 = 0 Reorder the terms: 114 + -26x + x2 = 0 Solving 114 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-114' to each side of the equation. 114 + -26x + -114 + x2 = 0 + -114 Reorder the terms: 114 + -114 + -26x + x2 = 0 + -114 Combine like terms: 114 + -114 = 0 0 + -26x + x2 = 0 + -114 -26x + x2 = 0 + -114 Combine like terms: 0 + -114 = -114 -26x + x2 = -114 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 = -114 + 169 Reorder the terms: 169 + -26x + x2 = -114 + 169 Combine like terms: -114 + 169 = 55 169 + -26x + x2 = 55 Factor a perfect square on the left side: (x + -13)(x + -13) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + -13) equal to 7.416198487 and -7.416198487.Subproblem 1
x + -13 = 7.416198487 Simplifying x + -13 = 7.416198487 Reorder the terms: -13 + x = 7.416198487 Solving -13 + x = 7.416198487 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 = 7.416198487 + 13 Combine like terms: -13 + 13 = 0 0 + x = 7.416198487 + 13 x = 7.416198487 + 13 Combine like terms: 7.416198487 + 13 = 20.416198487 x = 20.416198487 Simplifying x = 20.416198487Subproblem 2
x + -13 = -7.416198487 Simplifying x + -13 = -7.416198487 Reorder the terms: -13 + x = -7.416198487 Solving -13 + x = -7.416198487 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 = -7.416198487 + 13 Combine like terms: -13 + 13 = 0 0 + x = -7.416198487 + 13 x = -7.416198487 + 13 Combine like terms: -7.416198487 + 13 = 5.583801513 x = 5.583801513 Simplifying x = 5.583801513Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.416198487, 5.583801513}
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