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Simplifying x2 + -14x + 26 = 0 Reorder the terms: 26 + -14x + x2 = 0 Solving 26 + -14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -14x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + -14x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -14x + x2 = 0 + -26 -14x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 -14x + x2 = -26 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -26 + 49 Reorder the terms: 49 + -14x + x2 = -26 + 49 Combine like terms: -26 + 49 = 23 49 + -14x + x2 = 23 Factor a perfect square on the left side: (x + -7)(x + -7) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + -7) equal to 4.795831523 and -4.795831523.Subproblem 1
x + -7 = 4.795831523 Simplifying x + -7 = 4.795831523 Reorder the terms: -7 + x = 4.795831523 Solving -7 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 4.795831523 + 7 Combine like terms: -7 + 7 = 0 0 + x = 4.795831523 + 7 x = 4.795831523 + 7 Combine like terms: 4.795831523 + 7 = 11.795831523 x = 11.795831523 Simplifying x = 11.795831523Subproblem 2
x + -7 = -4.795831523 Simplifying x + -7 = -4.795831523 Reorder the terms: -7 + x = -4.795831523 Solving -7 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -4.795831523 + 7 Combine like terms: -7 + 7 = 0 0 + x = -4.795831523 + 7 x = -4.795831523 + 7 Combine like terms: -4.795831523 + 7 = 2.204168477 x = 2.204168477 Simplifying x = 2.204168477Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.795831523, 2.204168477}
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