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Simplifying x2 + -28x + 156 = 0 Reorder the terms: 156 + -28x + x2 = 0 Solving 156 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-156' to each side of the equation. 156 + -28x + -156 + x2 = 0 + -156 Reorder the terms: 156 + -156 + -28x + x2 = 0 + -156 Combine like terms: 156 + -156 = 0 0 + -28x + x2 = 0 + -156 -28x + x2 = 0 + -156 Combine like terms: 0 + -156 = -156 -28x + x2 = -156 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -156 + 196 Reorder the terms: 196 + -28x + x2 = -156 + 196 Combine like terms: -156 + 196 = 40 196 + -28x + x2 = 40 Factor a perfect square on the left side: (x + -14)(x + -14) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + -14) equal to 6.32455532 and -6.32455532.Subproblem 1
x + -14 = 6.32455532 Simplifying x + -14 = 6.32455532 Reorder the terms: -14 + x = 6.32455532 Solving -14 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 6.32455532 + 14 Combine like terms: -14 + 14 = 0 0 + x = 6.32455532 + 14 x = 6.32455532 + 14 Combine like terms: 6.32455532 + 14 = 20.32455532 x = 20.32455532 Simplifying x = 20.32455532Subproblem 2
x + -14 = -6.32455532 Simplifying x + -14 = -6.32455532 Reorder the terms: -14 + x = -6.32455532 Solving -14 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -6.32455532 + 14 Combine like terms: -14 + 14 = 0 0 + x = -6.32455532 + 14 x = -6.32455532 + 14 Combine like terms: -6.32455532 + 14 = 7.67544468 x = 7.67544468 Simplifying x = 7.67544468Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.32455532, 7.67544468}
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