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Simplifying 4.9x2 + 8x + -450 = 0 Reorder the terms: -450 + 8x + 4.9x2 = 0 Solving -450 + 8x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -91.83673469 + 1.632653061x + x2 = 0 Move the constant term to the right: Add '91.83673469' to each side of the equation. -91.83673469 + 1.632653061x + 91.83673469 + x2 = 0 + 91.83673469 Reorder the terms: -91.83673469 + 91.83673469 + 1.632653061x + x2 = 0 + 91.83673469 Combine like terms: -91.83673469 + 91.83673469 = 0.00000000 0.00000000 + 1.632653061x + x2 = 0 + 91.83673469 1.632653061x + x2 = 0 + 91.83673469 Combine like terms: 0 + 91.83673469 = 91.83673469 1.632653061x + x2 = 91.83673469 The x term is 1.632653061x. Take half its coefficient (0.8163265305). Square it (0.6663890044) and add it to both sides. Add '0.6663890044' to each side of the equation. 1.632653061x + 0.6663890044 + x2 = 91.83673469 + 0.6663890044 Reorder the terms: 0.6663890044 + 1.632653061x + x2 = 91.83673469 + 0.6663890044 Combine like terms: 91.83673469 + 0.6663890044 = 92.5031236944 0.6663890044 + 1.632653061x + x2 = 92.5031236944 Factor a perfect square on the left side: (x + 0.8163265305)(x + 0.8163265305) = 92.5031236944 Calculate the square root of the right side: 9.617854423 Break this problem into two subproblems by setting (x + 0.8163265305) equal to 9.617854423 and -9.617854423.Subproblem 1
x + 0.8163265305 = 9.617854423 Simplifying x + 0.8163265305 = 9.617854423 Reorder the terms: 0.8163265305 + x = 9.617854423 Solving 0.8163265305 + x = 9.617854423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8163265305' to each side of the equation. 0.8163265305 + -0.8163265305 + x = 9.617854423 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + x = 9.617854423 + -0.8163265305 x = 9.617854423 + -0.8163265305 Combine like terms: 9.617854423 + -0.8163265305 = 8.8015278925 x = 8.8015278925 Simplifying x = 8.8015278925Subproblem 2
x + 0.8163265305 = -9.617854423 Simplifying x + 0.8163265305 = -9.617854423 Reorder the terms: 0.8163265305 + x = -9.617854423 Solving 0.8163265305 + x = -9.617854423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8163265305' to each side of the equation. 0.8163265305 + -0.8163265305 + x = -9.617854423 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + x = -9.617854423 + -0.8163265305 x = -9.617854423 + -0.8163265305 Combine like terms: -9.617854423 + -0.8163265305 = -10.4341809535 x = -10.4341809535 Simplifying x = -10.4341809535Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.8015278925, -10.4341809535}
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