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Simplifying -0.0004x2 + -0.3x + 0.29 = 0 Reorder the terms: 0.29 + -0.3x + -0.0004x2 = 0 Solving 0.29 + -0.3x + -0.0004x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0004 the coefficient of the squared term: Divide each side by '-0.0004'. -725 + 750x + x2 = 0 Move the constant term to the right: Add '725' to each side of the equation. -725 + 750x + 725 + x2 = 0 + 725 Reorder the terms: -725 + 725 + 750x + x2 = 0 + 725 Combine like terms: -725 + 725 = 0 0 + 750x + x2 = 0 + 725 750x + x2 = 0 + 725 Combine like terms: 0 + 725 = 725 750x + x2 = 725 The x term is 750x. Take half its coefficient (375). Square it (140625) and add it to both sides. Add '140625' to each side of the equation. 750x + 140625 + x2 = 725 + 140625 Reorder the terms: 140625 + 750x + x2 = 725 + 140625 Combine like terms: 725 + 140625 = 141350 140625 + 750x + x2 = 141350 Factor a perfect square on the left side: (x + 375)(x + 375) = 141350 Calculate the square root of the right side: 375.965423942 Break this problem into two subproblems by setting (x + 375) equal to 375.965423942 and -375.965423942.Subproblem 1
x + 375 = 375.965423942 Simplifying x + 375 = 375.965423942 Reorder the terms: 375 + x = 375.965423942 Solving 375 + x = 375.965423942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-375' to each side of the equation. 375 + -375 + x = 375.965423942 + -375 Combine like terms: 375 + -375 = 0 0 + x = 375.965423942 + -375 x = 375.965423942 + -375 Combine like terms: 375.965423942 + -375 = 0.965423942 x = 0.965423942 Simplifying x = 0.965423942Subproblem 2
x + 375 = -375.965423942 Simplifying x + 375 = -375.965423942 Reorder the terms: 375 + x = -375.965423942 Solving 375 + x = -375.965423942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-375' to each side of the equation. 375 + -375 + x = -375.965423942 + -375 Combine like terms: 375 + -375 = 0 0 + x = -375.965423942 + -375 x = -375.965423942 + -375 Combine like terms: -375.965423942 + -375 = -750.965423942 x = -750.965423942 Simplifying x = -750.965423942Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.965423942, -750.965423942}
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