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Simplifying x2 + -12x + 13 = 0 Reorder the terms: 13 + -12x + x2 = 0 Solving 13 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -12x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -12x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -12x + x2 = 0 + -13 -12x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -12x + x2 = -13 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -13 + 36 Reorder the terms: 36 + -12x + x2 = -13 + 36 Combine like terms: -13 + 36 = 23 36 + -12x + x2 = 23 Factor a perfect square on the left side: (x + -6)(x + -6) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + -6) equal to 4.795831523 and -4.795831523.Subproblem 1
x + -6 = 4.795831523 Simplifying x + -6 = 4.795831523 Reorder the terms: -6 + x = 4.795831523 Solving -6 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 4.795831523 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.795831523 + 6 x = 4.795831523 + 6 Combine like terms: 4.795831523 + 6 = 10.795831523 x = 10.795831523 Simplifying x = 10.795831523Subproblem 2
x + -6 = -4.795831523 Simplifying x + -6 = -4.795831523 Reorder the terms: -6 + x = -4.795831523 Solving -6 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -4.795831523 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.795831523 + 6 x = -4.795831523 + 6 Combine like terms: -4.795831523 + 6 = 1.204168477 x = 1.204168477 Simplifying x = 1.204168477Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.795831523, 1.204168477}
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