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Simplifying x2 + -26x + -376 = 0 Reorder the terms: -376 + -26x + x2 = 0 Solving -376 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '376' to each side of the equation. -376 + -26x + 376 + x2 = 0 + 376 Reorder the terms: -376 + 376 + -26x + x2 = 0 + 376 Combine like terms: -376 + 376 = 0 0 + -26x + x2 = 0 + 376 -26x + x2 = 0 + 376 Combine like terms: 0 + 376 = 376 -26x + x2 = 376 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 = 376 + 169 Reorder the terms: 169 + -26x + x2 = 376 + 169 Combine like terms: 376 + 169 = 545 169 + -26x + x2 = 545 Factor a perfect square on the left side: (x + -13)(x + -13) = 545 Calculate the square root of the right side: 23.34523506 Break this problem into two subproblems by setting (x + -13) equal to 23.34523506 and -23.34523506.Subproblem 1
x + -13 = 23.34523506 Simplifying x + -13 = 23.34523506 Reorder the terms: -13 + x = 23.34523506 Solving -13 + x = 23.34523506 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 = 23.34523506 + 13 Combine like terms: -13 + 13 = 0 0 + x = 23.34523506 + 13 x = 23.34523506 + 13 Combine like terms: 23.34523506 + 13 = 36.34523506 x = 36.34523506 Simplifying x = 36.34523506Subproblem 2
x + -13 = -23.34523506 Simplifying x + -13 = -23.34523506 Reorder the terms: -13 + x = -23.34523506 Solving -13 + x = -23.34523506 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 = -23.34523506 + 13 Combine like terms: -13 + 13 = 0 0 + x = -23.34523506 + 13 x = -23.34523506 + 13 Combine like terms: -23.34523506 + 13 = -10.34523506 x = -10.34523506 Simplifying x = -10.34523506Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.34523506, -10.34523506}
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