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Simplifying 0 = -4.9x2 + 8x + 100 Reorder the terms: 0 = 100 + 8x + -4.9x2 Solving 0 = 100 + 8x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + -8x + 4.9x2 = 100 + 8x + -4.9x2 + -100 + -8x + 4.9x2 Reorder the terms: -100 + -8x + 4.9x2 = 100 + -100 + 8x + -8x + -4.9x2 + 4.9x2 Combine like terms: 100 + -100 = 0 -100 + -8x + 4.9x2 = 0 + 8x + -8x + -4.9x2 + 4.9x2 -100 + -8x + 4.9x2 = 8x + -8x + -4.9x2 + 4.9x2 Combine like terms: 8x + -8x = 0 -100 + -8x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -100 + -8x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -100 + -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'. -20.40816327 + -1.632653061x + x2 = 0 Move the constant term to the right: Add '20.40816327' to each side of the equation. -20.40816327 + -1.632653061x + 20.40816327 + x2 = 0 + 20.40816327 Reorder the terms: -20.40816327 + 20.40816327 + -1.632653061x + x2 = 0 + 20.40816327 Combine like terms: -20.40816327 + 20.40816327 = 0.00000000 0.00000000 + -1.632653061x + x2 = 0 + 20.40816327 -1.632653061x + x2 = 0 + 20.40816327 Combine like terms: 0 + 20.40816327 = 20.40816327 -1.632653061x + x2 = 20.40816327 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 = 20.40816327 + 0.6663890044 Reorder the terms: 0.6663890044 + -1.632653061x + x2 = 20.40816327 + 0.6663890044 Combine like terms: 20.40816327 + 0.6663890044 = 21.0745522744 0.6663890044 + -1.632653061x + x2 = 21.0745522744 Factor a perfect square on the left side: (x + -0.8163265305)(x + -0.8163265305) = 21.0745522744 Calculate the square root of the right side: 4.590702808 Break this problem into two subproblems by setting (x + -0.8163265305) equal to 4.590702808 and -4.590702808.Subproblem 1
x + -0.8163265305 = 4.590702808 Simplifying x + -0.8163265305 = 4.590702808 Reorder the terms: -0.8163265305 + x = 4.590702808 Solving -0.8163265305 + x = 4.590702808 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 = 4.590702808 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = 4.590702808 + 0.8163265305 x = 4.590702808 + 0.8163265305 Combine like terms: 4.590702808 + 0.8163265305 = 5.4070293385 x = 5.4070293385 Simplifying x = 5.4070293385Subproblem 2
x + -0.8163265305 = -4.590702808 Simplifying x + -0.8163265305 = -4.590702808 Reorder the terms: -0.8163265305 + x = -4.590702808 Solving -0.8163265305 + x = -4.590702808 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 = -4.590702808 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = -4.590702808 + 0.8163265305 x = -4.590702808 + 0.8163265305 Combine like terms: -4.590702808 + 0.8163265305 = -3.7743762775 x = -3.7743762775 Simplifying x = -3.7743762775Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.4070293385, -3.7743762775}
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