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Simplifying 0.2x2 + -64.1x + -30 = 0 Reorder the terms: -30 + -64.1x + 0.2x2 = 0 Solving -30 + -64.1x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -150 + -320.5x + x2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + -320.5x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + -320.5x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + -320.5x + x2 = 0 + 150 -320.5x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 -320.5x + x2 = 150 The x term is -320.5x. Take half its coefficient (-160.25). Square it (25680.0625) and add it to both sides. Add '25680.0625' to each side of the equation. -320.5x + 25680.0625 + x2 = 150 + 25680.0625 Reorder the terms: 25680.0625 + -320.5x + x2 = 150 + 25680.0625 Combine like terms: 150 + 25680.0625 = 25830.0625 25680.0625 + -320.5x + x2 = 25830.0625 Factor a perfect square on the left side: (x + -160.25)(x + -160.25) = 25830.0625 Calculate the square root of the right side: 160.717337273 Break this problem into two subproblems by setting (x + -160.25) equal to 160.717337273 and -160.717337273.Subproblem 1
x + -160.25 = 160.717337273 Simplifying x + -160.25 = 160.717337273 Reorder the terms: -160.25 + x = 160.717337273 Solving -160.25 + x = 160.717337273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '160.25' to each side of the equation. -160.25 + 160.25 + x = 160.717337273 + 160.25 Combine like terms: -160.25 + 160.25 = 0.00 0.00 + x = 160.717337273 + 160.25 x = 160.717337273 + 160.25 Combine like terms: 160.717337273 + 160.25 = 320.967337273 x = 320.967337273 Simplifying x = 320.967337273Subproblem 2
x + -160.25 = -160.717337273 Simplifying x + -160.25 = -160.717337273 Reorder the terms: -160.25 + x = -160.717337273 Solving -160.25 + x = -160.717337273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '160.25' to each side of the equation. -160.25 + 160.25 + x = -160.717337273 + 160.25 Combine like terms: -160.25 + 160.25 = 0.00 0.00 + x = -160.717337273 + 160.25 x = -160.717337273 + 160.25 Combine like terms: -160.717337273 + 160.25 = -0.467337273 x = -0.467337273 Simplifying x = -0.467337273Solution
The solution to the problem is based on the solutions from the subproblems. x = {320.967337273, -0.467337273}
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