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Simplifying -1x2 + -10x + 150 = 0 Reorder the terms: 150 + -10x + -1x2 = 0 Solving 150 + -10x + -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 + 10x + x2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + 10x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 10x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 10x + x2 = 0 + 150 10x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 10x + x2 = 150 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 150 + 25 Reorder the terms: 25 + 10x + x2 = 150 + 25 Combine like terms: 150 + 25 = 175 25 + 10x + x2 = 175 Factor a perfect square on the left side: (x + 5)(x + 5) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (x + 5) equal to 13.228756555 and -13.228756555.Subproblem 1
x + 5 = 13.228756555 Simplifying x + 5 = 13.228756555 Reorder the terms: 5 + x = 13.228756555 Solving 5 + x = 13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 13.228756555 + -5 Combine like terms: 5 + -5 = 0 0 + x = 13.228756555 + -5 x = 13.228756555 + -5 Combine like terms: 13.228756555 + -5 = 8.228756555 x = 8.228756555 Simplifying x = 8.228756555Subproblem 2
x + 5 = -13.228756555 Simplifying x + 5 = -13.228756555 Reorder the terms: 5 + x = -13.228756555 Solving 5 + x = -13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -13.228756555 + -5 Combine like terms: 5 + -5 = 0 0 + x = -13.228756555 + -5 x = -13.228756555 + -5 Combine like terms: -13.228756555 + -5 = -18.228756555 x = -18.228756555 Simplifying x = -18.228756555Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.228756555, -18.228756555}
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