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Simplifying 3 = 8x + -4.9x2 Solving 3 = 8x + -4.9x2 Solving for variable 'x'. Reorder the terms: 3 + -8x + 4.9x2 = 8x + -8x + -4.9x2 + 4.9x2 Combine like terms: 8x + -8x = 0 3 + -8x + 4.9x2 = 0 + -4.9x2 + 4.9x2 3 + -8x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 3 + -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'. 0.612244898 + -1.632653061x + x2 = 0 Move the constant term to the right: Add '-0.612244898' to each side of the equation. 0.612244898 + -1.632653061x + -0.612244898 + x2 = 0 + -0.612244898 Reorder the terms: 0.612244898 + -0.612244898 + -1.632653061x + x2 = 0 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + -1.632653061x + x2 = 0 + -0.612244898 -1.632653061x + x2 = 0 + -0.612244898 Combine like terms: 0 + -0.612244898 = -0.612244898 -1.632653061x + x2 = -0.612244898 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 = -0.612244898 + 0.6663890044 Reorder the terms: 0.6663890044 + -1.632653061x + x2 = -0.612244898 + 0.6663890044 Combine like terms: -0.612244898 + 0.6663890044 = 0.0541441064 0.6663890044 + -1.632653061x + x2 = 0.0541441064 Factor a perfect square on the left side: (x + -0.8163265305)(x + -0.8163265305) = 0.0541441064 Calculate the square root of the right side: 0.232688862 Break this problem into two subproblems by setting (x + -0.8163265305) equal to 0.232688862 and -0.232688862.Subproblem 1
x + -0.8163265305 = 0.232688862 Simplifying x + -0.8163265305 = 0.232688862 Reorder the terms: -0.8163265305 + x = 0.232688862 Solving -0.8163265305 + x = 0.232688862 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 = 0.232688862 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = 0.232688862 + 0.8163265305 x = 0.232688862 + 0.8163265305 Combine like terms: 0.232688862 + 0.8163265305 = 1.0490153925 x = 1.0490153925 Simplifying x = 1.0490153925Subproblem 2
x + -0.8163265305 = -0.232688862 Simplifying x + -0.8163265305 = -0.232688862 Reorder the terms: -0.8163265305 + x = -0.232688862 Solving -0.8163265305 + x = -0.232688862 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 = -0.232688862 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = -0.232688862 + 0.8163265305 x = -0.232688862 + 0.8163265305 Combine like terms: -0.232688862 + 0.8163265305 = 0.5836376685 x = 0.5836376685 Simplifying x = 0.5836376685Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0490153925, 0.5836376685}
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