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Simplifying -4.9x2 + 8x + 9.12 = 0 Reorder the terms: 9.12 + 8x + -4.9x2 = 0 Solving 9.12 + 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'. -1.86122449 + -1.632653061x + x2 = 0 Move the constant term to the right: Add '1.86122449' to each side of the equation. -1.86122449 + -1.632653061x + 1.86122449 + x2 = 0 + 1.86122449 Reorder the terms: -1.86122449 + 1.86122449 + -1.632653061x + x2 = 0 + 1.86122449 Combine like terms: -1.86122449 + 1.86122449 = 0.00000000 0.00000000 + -1.632653061x + x2 = 0 + 1.86122449 -1.632653061x + x2 = 0 + 1.86122449 Combine like terms: 0 + 1.86122449 = 1.86122449 -1.632653061x + x2 = 1.86122449 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 = 1.86122449 + 0.6663890044 Reorder the terms: 0.6663890044 + -1.632653061x + x2 = 1.86122449 + 0.6663890044 Combine like terms: 1.86122449 + 0.6663890044 = 2.5276134944 0.6663890044 + -1.632653061x + x2 = 2.5276134944 Factor a perfect square on the left side: (x + -0.8163265305)(x + -0.8163265305) = 2.5276134944 Calculate the square root of the right side: 1.589847003 Break this problem into two subproblems by setting (x + -0.8163265305) equal to 1.589847003 and -1.589847003.Subproblem 1
x + -0.8163265305 = 1.589847003 Simplifying x + -0.8163265305 = 1.589847003 Reorder the terms: -0.8163265305 + x = 1.589847003 Solving -0.8163265305 + x = 1.589847003 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 = 1.589847003 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = 1.589847003 + 0.8163265305 x = 1.589847003 + 0.8163265305 Combine like terms: 1.589847003 + 0.8163265305 = 2.4061735335 x = 2.4061735335 Simplifying x = 2.4061735335Subproblem 2
x + -0.8163265305 = -1.589847003 Simplifying x + -0.8163265305 = -1.589847003 Reorder the terms: -0.8163265305 + x = -1.589847003 Solving -0.8163265305 + x = -1.589847003 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 = -1.589847003 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = -1.589847003 + 0.8163265305 x = -1.589847003 + 0.8163265305 Combine like terms: -1.589847003 + 0.8163265305 = -0.7735204725 x = -0.7735204725 Simplifying x = -0.7735204725Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4061735335, -0.7735204725}
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