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Simplifying -1x2 + 28x + -150 = 0 Reorder the terms: -150 + 28x + -1x2 = 0 Solving -150 + 28x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 150 + -28x + x2 = 0 Move the constant term to the right: Add '-150' to each side of the equation. 150 + -28x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + -28x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -28x + x2 = 0 + -150 -28x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 -28x + x2 = -150 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 = -150 + 196 Reorder the terms: 196 + -28x + x2 = -150 + 196 Combine like terms: -150 + 196 = 46 196 + -28x + x2 = 46 Factor a perfect square on the left side: (x + -14)(x + -14) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + -14) equal to 6.782329983 and -6.782329983.Subproblem 1
x + -14 = 6.782329983 Simplifying x + -14 = 6.782329983 Reorder the terms: -14 + x = 6.782329983 Solving -14 + x = 6.782329983 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 = 6.782329983 + 14 Combine like terms: -14 + 14 = 0 0 + x = 6.782329983 + 14 x = 6.782329983 + 14 Combine like terms: 6.782329983 + 14 = 20.782329983 x = 20.782329983 Simplifying x = 20.782329983Subproblem 2
x + -14 = -6.782329983 Simplifying x + -14 = -6.782329983 Reorder the terms: -14 + x = -6.782329983 Solving -14 + x = -6.782329983 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 = -6.782329983 + 14 Combine like terms: -14 + 14 = 0 0 + x = -6.782329983 + 14 x = -6.782329983 + 14 Combine like terms: -6.782329983 + 14 = 7.217670017 x = 7.217670017 Simplifying x = 7.217670017Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.782329983, 7.217670017}
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