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Simplifying X2 + -26X + 169 = 12 Reorder the terms: 169 + -26X + X2 = 12 Solving 169 + -26X + X2 = 12 Solving for variable 'X'. Reorder the terms: 169 + -12 + -26X + X2 = 12 + -12 Combine like terms: 169 + -12 = 157 157 + -26X + X2 = 12 + -12 Combine like terms: 12 + -12 = 0 157 + -26X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-157' to each side of the equation. 157 + -26X + -157 + X2 = 0 + -157 Reorder the terms: 157 + -157 + -26X + X2 = 0 + -157 Combine like terms: 157 + -157 = 0 0 + -26X + X2 = 0 + -157 -26X + X2 = 0 + -157 Combine like terms: 0 + -157 = -157 -26X + X2 = -157 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 = -157 + 169 Reorder the terms: 169 + -26X + X2 = -157 + 169 Combine like terms: -157 + 169 = 12 169 + -26X + X2 = 12 Factor a perfect square on the left side: (X + -13)(X + -13) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (X + -13) equal to 3.464101615 and -3.464101615.Subproblem 1
X + -13 = 3.464101615 Simplifying X + -13 = 3.464101615 Reorder the terms: -13 + X = 3.464101615 Solving -13 + X = 3.464101615 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 = 3.464101615 + 13 Combine like terms: -13 + 13 = 0 0 + X = 3.464101615 + 13 X = 3.464101615 + 13 Combine like terms: 3.464101615 + 13 = 16.464101615 X = 16.464101615 Simplifying X = 16.464101615Subproblem 2
X + -13 = -3.464101615 Simplifying X + -13 = -3.464101615 Reorder the terms: -13 + X = -3.464101615 Solving -13 + X = -3.464101615 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 = -3.464101615 + 13 Combine like terms: -13 + 13 = 0 0 + X = -3.464101615 + 13 X = -3.464101615 + 13 Combine like terms: -3.464101615 + 13 = 9.535898385 X = 9.535898385 Simplifying X = 9.535898385Solution
The solution to the problem is based on the solutions from the subproblems. X = {16.464101615, 9.535898385}
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