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Simplifying 0.0925x2 + -1.3x + -478.6 = 0 Reorder the terms: -478.6 + -1.3x + 0.0925x2 = 0 Solving -478.6 + -1.3x + 0.0925x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0925 the coefficient of the squared term: Divide each side by '0.0925'. -5174.054054 + -14.05405405x + x2 = 0 Move the constant term to the right: Add '5174.054054' to each side of the equation. -5174.054054 + -14.05405405x + 5174.054054 + x2 = 0 + 5174.054054 Reorder the terms: -5174.054054 + 5174.054054 + -14.05405405x + x2 = 0 + 5174.054054 Combine like terms: -5174.054054 + 5174.054054 = 0.000000 0.000000 + -14.05405405x + x2 = 0 + 5174.054054 -14.05405405x + x2 = 0 + 5174.054054 Combine like terms: 0 + 5174.054054 = 5174.054054 -14.05405405x + x2 = 5174.054054 The x term is -14.05405405x. Take half its coefficient (-7.027027025). Square it (49.37910881) and add it to both sides. Add '49.37910881' to each side of the equation. -14.05405405x + 49.37910881 + x2 = 5174.054054 + 49.37910881 Reorder the terms: 49.37910881 + -14.05405405x + x2 = 5174.054054 + 49.37910881 Combine like terms: 5174.054054 + 49.37910881 = 5223.43316281 49.37910881 + -14.05405405x + x2 = 5223.43316281 Factor a perfect square on the left side: (x + -7.027027025)(x + -7.027027025) = 5223.43316281 Calculate the square root of the right side: 72.273322622 Break this problem into two subproblems by setting (x + -7.027027025) equal to 72.273322622 and -72.273322622.Subproblem 1
x + -7.027027025 = 72.273322622 Simplifying x + -7.027027025 = 72.273322622 Reorder the terms: -7.027027025 + x = 72.273322622 Solving -7.027027025 + x = 72.273322622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.027027025' to each side of the equation. -7.027027025 + 7.027027025 + x = 72.273322622 + 7.027027025 Combine like terms: -7.027027025 + 7.027027025 = 0.000000000 0.000000000 + x = 72.273322622 + 7.027027025 x = 72.273322622 + 7.027027025 Combine like terms: 72.273322622 + 7.027027025 = 79.300349647 x = 79.300349647 Simplifying x = 79.300349647Subproblem 2
x + -7.027027025 = -72.273322622 Simplifying x + -7.027027025 = -72.273322622 Reorder the terms: -7.027027025 + x = -72.273322622 Solving -7.027027025 + x = -72.273322622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.027027025' to each side of the equation. -7.027027025 + 7.027027025 + x = -72.273322622 + 7.027027025 Combine like terms: -7.027027025 + 7.027027025 = 0.000000000 0.000000000 + x = -72.273322622 + 7.027027025 x = -72.273322622 + 7.027027025 Combine like terms: -72.273322622 + 7.027027025 = -65.246295597 x = -65.246295597 Simplifying x = -65.246295597Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.300349647, -65.246295597}
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