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Simplifying 0 = -4.9x2 + 8x + 1 Reorder the terms: 0 = 1 + 8x + -4.9x2 Solving 0 = 1 + 8x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -8x + 4.9x2 = 1 + 8x + -4.9x2 + -1 + -8x + 4.9x2 Reorder the terms: -1 + -8x + 4.9x2 = 1 + -1 + 8x + -8x + -4.9x2 + 4.9x2 Combine like terms: 1 + -1 = 0 -1 + -8x + 4.9x2 = 0 + 8x + -8x + -4.9x2 + 4.9x2 -1 + -8x + 4.9x2 = 8x + -8x + -4.9x2 + 4.9x2 Combine like terms: 8x + -8x = 0 -1 + -8x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -1 + -8x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -1 + -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'. -0.2040816327 + -1.632653061x + x2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -1.632653061x + 0.2040816327 + x2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -1.632653061x + x2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -1.632653061x + x2 = 0 + 0.2040816327 -1.632653061x + x2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -1.632653061x + x2 = 0.2040816327 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 = 0.2040816327 + 0.6663890044 Reorder the terms: 0.6663890044 + -1.632653061x + x2 = 0.2040816327 + 0.6663890044 Combine like terms: 0.2040816327 + 0.6663890044 = 0.8704706371 0.6663890044 + -1.632653061x + x2 = 0.8704706371 Factor a perfect square on the left side: (x + -0.8163265305)(x + -0.8163265305) = 0.8704706371 Calculate the square root of the right side: 0.932990159 Break this problem into two subproblems by setting (x + -0.8163265305) equal to 0.932990159 and -0.932990159.Subproblem 1
x + -0.8163265305 = 0.932990159 Simplifying x + -0.8163265305 = 0.932990159 Reorder the terms: -0.8163265305 + x = 0.932990159 Solving -0.8163265305 + x = 0.932990159 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 = 0.932990159 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = 0.932990159 + 0.8163265305 x = 0.932990159 + 0.8163265305 Combine like terms: 0.932990159 + 0.8163265305 = 1.7493166895 x = 1.7493166895 Simplifying x = 1.7493166895Subproblem 2
x + -0.8163265305 = -0.932990159 Simplifying x + -0.8163265305 = -0.932990159 Reorder the terms: -0.8163265305 + x = -0.932990159 Solving -0.8163265305 + x = -0.932990159 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 = -0.932990159 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = -0.932990159 + 0.8163265305 x = -0.932990159 + 0.8163265305 Combine like terms: -0.932990159 + 0.8163265305 = -0.1166636285 x = -0.1166636285 Simplifying x = -0.1166636285Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7493166895, -0.1166636285}
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