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Simplifying -8.7x2 + 150x + 1666 = 0 Reorder the terms: 1666 + 150x + -8.7x2 = 0 Solving 1666 + 150x + -8.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8.7 the coefficient of the squared term: Divide each side by '-8.7'. -191.4942529 + -17.24137931x + x2 = 0 Move the constant term to the right: Add '191.4942529' to each side of the equation. -191.4942529 + -17.24137931x + 191.4942529 + x2 = 0 + 191.4942529 Reorder the terms: -191.4942529 + 191.4942529 + -17.24137931x + x2 = 0 + 191.4942529 Combine like terms: -191.4942529 + 191.4942529 = 0.0000000 0.0000000 + -17.24137931x + x2 = 0 + 191.4942529 -17.24137931x + x2 = 0 + 191.4942529 Combine like terms: 0 + 191.4942529 = 191.4942529 -17.24137931x + x2 = 191.4942529 The x term is -17.24137931x. Take half its coefficient (-8.620689655). Square it (74.31629013) and add it to both sides. Add '74.31629013' to each side of the equation. -17.24137931x + 74.31629013 + x2 = 191.4942529 + 74.31629013 Reorder the terms: 74.31629013 + -17.24137931x + x2 = 191.4942529 + 74.31629013 Combine like terms: 191.4942529 + 74.31629013 = 265.81054303 74.31629013 + -17.24137931x + x2 = 265.81054303 Factor a perfect square on the left side: (x + -8.620689655)(x + -8.620689655) = 265.81054303 Calculate the square root of the right side: 16.30369722 Break this problem into two subproblems by setting (x + -8.620689655) equal to 16.30369722 and -16.30369722.Subproblem 1
x + -8.620689655 = 16.30369722 Simplifying x + -8.620689655 = 16.30369722 Reorder the terms: -8.620689655 + x = 16.30369722 Solving -8.620689655 + x = 16.30369722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.620689655' to each side of the equation. -8.620689655 + 8.620689655 + x = 16.30369722 + 8.620689655 Combine like terms: -8.620689655 + 8.620689655 = 0.000000000 0.000000000 + x = 16.30369722 + 8.620689655 x = 16.30369722 + 8.620689655 Combine like terms: 16.30369722 + 8.620689655 = 24.924386875 x = 24.924386875 Simplifying x = 24.924386875Subproblem 2
x + -8.620689655 = -16.30369722 Simplifying x + -8.620689655 = -16.30369722 Reorder the terms: -8.620689655 + x = -16.30369722 Solving -8.620689655 + x = -16.30369722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.620689655' to each side of the equation. -8.620689655 + 8.620689655 + x = -16.30369722 + 8.620689655 Combine like terms: -8.620689655 + 8.620689655 = 0.000000000 0.000000000 + x = -16.30369722 + 8.620689655 x = -16.30369722 + 8.620689655 Combine like terms: -16.30369722 + 8.620689655 = -7.683007565 x = -7.683007565 Simplifying x = -7.683007565Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.924386875, -7.683007565}
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