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Simplifying -1x2 + -30x + -112.5 = 0 Reorder the terms: -112.5 + -30x + -1x2 = 0 Solving -112.5 + -30x + -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'. 112.5 + 30x + x2 = 0 Move the constant term to the right: Add '-112.5' to each side of the equation. 112.5 + 30x + -112.5 + x2 = 0 + -112.5 Reorder the terms: 112.5 + -112.5 + 30x + x2 = 0 + -112.5 Combine like terms: 112.5 + -112.5 = 0.0 0.0 + 30x + x2 = 0 + -112.5 30x + x2 = 0 + -112.5 Combine like terms: 0 + -112.5 = -112.5 30x + x2 = -112.5 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -112.5 + 225 Reorder the terms: 225 + 30x + x2 = -112.5 + 225 Combine like terms: -112.5 + 225 = 112.5 225 + 30x + x2 = 112.5 Factor a perfect square on the left side: (x + 15)(x + 15) = 112.5 Calculate the square root of the right side: 10.606601718 Break this problem into two subproblems by setting (x + 15) equal to 10.606601718 and -10.606601718.Subproblem 1
x + 15 = 10.606601718 Simplifying x + 15 = 10.606601718 Reorder the terms: 15 + x = 10.606601718 Solving 15 + x = 10.606601718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 10.606601718 + -15 Combine like terms: 15 + -15 = 0 0 + x = 10.606601718 + -15 x = 10.606601718 + -15 Combine like terms: 10.606601718 + -15 = -4.393398282 x = -4.393398282 Simplifying x = -4.393398282Subproblem 2
x + 15 = -10.606601718 Simplifying x + 15 = -10.606601718 Reorder the terms: 15 + x = -10.606601718 Solving 15 + x = -10.606601718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -10.606601718 + -15 Combine like terms: 15 + -15 = 0 0 + x = -10.606601718 + -15 x = -10.606601718 + -15 Combine like terms: -10.606601718 + -15 = -25.606601718 x = -25.606601718 Simplifying x = -25.606601718Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.393398282, -25.606601718}
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