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Simplifying 3 + 25.3x + -4.9x2 = 0 Solving 3 + 25.3x + -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'. -0.612244898 + -5.163265306x + x2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -5.163265306x + 0.612244898 + x2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -5.163265306x + x2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -5.163265306x + x2 = 0 + 0.612244898 -5.163265306x + x2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -5.163265306x + x2 = 0.612244898 The x term is -5.163265306x. Take half its coefficient (-2.581632653). Square it (6.664827155) and add it to both sides. Add '6.664827155' to each side of the equation. -5.163265306x + 6.664827155 + x2 = 0.612244898 + 6.664827155 Reorder the terms: 6.664827155 + -5.163265306x + x2 = 0.612244898 + 6.664827155 Combine like terms: 0.612244898 + 6.664827155 = 7.277072053 6.664827155 + -5.163265306x + x2 = 7.277072053 Factor a perfect square on the left side: (x + -2.581632653)(x + -2.581632653) = 7.277072053 Calculate the square root of the right side: 2.697604873 Break this problem into two subproblems by setting (x + -2.581632653) equal to 2.697604873 and -2.697604873.Subproblem 1
x + -2.581632653 = 2.697604873 Simplifying x + -2.581632653 = 2.697604873 Reorder the terms: -2.581632653 + x = 2.697604873 Solving -2.581632653 + x = 2.697604873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.581632653' to each side of the equation. -2.581632653 + 2.581632653 + x = 2.697604873 + 2.581632653 Combine like terms: -2.581632653 + 2.581632653 = 0.000000000 0.000000000 + x = 2.697604873 + 2.581632653 x = 2.697604873 + 2.581632653 Combine like terms: 2.697604873 + 2.581632653 = 5.279237526 x = 5.279237526 Simplifying x = 5.279237526Subproblem 2
x + -2.581632653 = -2.697604873 Simplifying x + -2.581632653 = -2.697604873 Reorder the terms: -2.581632653 + x = -2.697604873 Solving -2.581632653 + x = -2.697604873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.581632653' to each side of the equation. -2.581632653 + 2.581632653 + x = -2.697604873 + 2.581632653 Combine like terms: -2.581632653 + 2.581632653 = 0.000000000 0.000000000 + x = -2.697604873 + 2.581632653 x = -2.697604873 + 2.581632653 Combine like terms: -2.697604873 + 2.581632653 = -0.11597222 x = -0.11597222 Simplifying x = -0.11597222Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.279237526, -0.11597222}
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