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Simplifying 0 = -4.9x2 + 8x + -1.5 Reorder the terms: 0 = -1.5 + 8x + -4.9x2 Solving 0 = -1.5 + 8x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + 1.5 = 1.5 1.5 + -8x + 4.9x2 = -1.5 + 8x + -4.9x2 + 1.5 + -8x + 4.9x2 Reorder the terms: 1.5 + -8x + 4.9x2 = -1.5 + 1.5 + 8x + -8x + -4.9x2 + 4.9x2 Combine like terms: -1.5 + 1.5 = 0.0 1.5 + -8x + 4.9x2 = 0.0 + 8x + -8x + -4.9x2 + 4.9x2 1.5 + -8x + 4.9x2 = 8x + -8x + -4.9x2 + 4.9x2 Combine like terms: 8x + -8x = 0 1.5 + -8x + 4.9x2 = 0 + -4.9x2 + 4.9x2 1.5 + -8x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 1.5 + -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'. 0.306122449 + -1.632653061x + x2 = 0 Move the constant term to the right: Add '-0.306122449' to each side of the equation. 0.306122449 + -1.632653061x + -0.306122449 + x2 = 0 + -0.306122449 Reorder the terms: 0.306122449 + -0.306122449 + -1.632653061x + x2 = 0 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + -1.632653061x + x2 = 0 + -0.306122449 -1.632653061x + x2 = 0 + -0.306122449 Combine like terms: 0 + -0.306122449 = -0.306122449 -1.632653061x + x2 = -0.306122449 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 = -0.306122449 + 0.6663890044 Reorder the terms: 0.6663890044 + -1.632653061x + x2 = -0.306122449 + 0.6663890044 Combine like terms: -0.306122449 + 0.6663890044 = 0.3602665554 0.6663890044 + -1.632653061x + x2 = 0.3602665554 Factor a perfect square on the left side: (x + -0.8163265305)(x + -0.8163265305) = 0.3602665554 Calculate the square root of the right side: 0.600222088 Break this problem into two subproblems by setting (x + -0.8163265305) equal to 0.600222088 and -0.600222088.Subproblem 1
x + -0.8163265305 = 0.600222088 Simplifying x + -0.8163265305 = 0.600222088 Reorder the terms: -0.8163265305 + x = 0.600222088 Solving -0.8163265305 + x = 0.600222088 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 = 0.600222088 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = 0.600222088 + 0.8163265305 x = 0.600222088 + 0.8163265305 Combine like terms: 0.600222088 + 0.8163265305 = 1.4165486185 x = 1.4165486185 Simplifying x = 1.4165486185Subproblem 2
x + -0.8163265305 = -0.600222088 Simplifying x + -0.8163265305 = -0.600222088 Reorder the terms: -0.8163265305 + x = -0.600222088 Solving -0.8163265305 + x = -0.600222088 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 = -0.600222088 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = -0.600222088 + 0.8163265305 x = -0.600222088 + 0.8163265305 Combine like terms: -0.600222088 + 0.8163265305 = 0.2161044425 x = 0.2161044425 Simplifying x = 0.2161044425Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4165486185, 0.2161044425}
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