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Simplifying 650 = 8x + 4.9x2 Solving 650 = 8x + 4.9x2 Solving for variable 'x'. Reorder the terms: 650 + -8x + -4.9x2 = 8x + -8x + 4.9x2 + -4.9x2 Combine like terms: 8x + -8x = 0 650 + -8x + -4.9x2 = 0 + 4.9x2 + -4.9x2 650 + -8x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 650 + -8x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -132.6530612 + 1.632653061x + x2 = 0 Move the constant term to the right: Add '132.6530612' to each side of the equation. -132.6530612 + 1.632653061x + 132.6530612 + x2 = 0 + 132.6530612 Reorder the terms: -132.6530612 + 132.6530612 + 1.632653061x + x2 = 0 + 132.6530612 Combine like terms: -132.6530612 + 132.6530612 = 0.0000000 0.0000000 + 1.632653061x + x2 = 0 + 132.6530612 1.632653061x + x2 = 0 + 132.6530612 Combine like terms: 0 + 132.6530612 = 132.6530612 1.632653061x + x2 = 132.6530612 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 = 132.6530612 + 0.6663890044 Reorder the terms: 0.6663890044 + 1.632653061x + x2 = 132.6530612 + 0.6663890044 Combine like terms: 132.6530612 + 0.6663890044 = 133.3194502044 0.6663890044 + 1.632653061x + x2 = 133.3194502044 Factor a perfect square on the left side: (x + 0.8163265305)(x + 0.8163265305) = 133.3194502044 Calculate the square root of the right side: 11.546404211 Break this problem into two subproblems by setting (x + 0.8163265305) equal to 11.546404211 and -11.546404211.Subproblem 1
x + 0.8163265305 = 11.546404211 Simplifying x + 0.8163265305 = 11.546404211 Reorder the terms: 0.8163265305 + x = 11.546404211 Solving 0.8163265305 + x = 11.546404211 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 = 11.546404211 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + x = 11.546404211 + -0.8163265305 x = 11.546404211 + -0.8163265305 Combine like terms: 11.546404211 + -0.8163265305 = 10.7300776805 x = 10.7300776805 Simplifying x = 10.7300776805Subproblem 2
x + 0.8163265305 = -11.546404211 Simplifying x + 0.8163265305 = -11.546404211 Reorder the terms: 0.8163265305 + x = -11.546404211 Solving 0.8163265305 + x = -11.546404211 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 = -11.546404211 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + x = -11.546404211 + -0.8163265305 x = -11.546404211 + -0.8163265305 Combine like terms: -11.546404211 + -0.8163265305 = -12.3627307415 x = -12.3627307415 Simplifying x = -12.3627307415Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.7300776805, -12.3627307415}
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