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Simplifying 0 = -4.9x2 + 8x + 700 Reorder the terms: 0 = 700 + 8x + -4.9x2 Solving 0 = 700 + 8x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -700 = -700 -700 + -8x + 4.9x2 = 700 + 8x + -4.9x2 + -700 + -8x + 4.9x2 Reorder the terms: -700 + -8x + 4.9x2 = 700 + -700 + 8x + -8x + -4.9x2 + 4.9x2 Combine like terms: 700 + -700 = 0 -700 + -8x + 4.9x2 = 0 + 8x + -8x + -4.9x2 + 4.9x2 -700 + -8x + 4.9x2 = 8x + -8x + -4.9x2 + 4.9x2 Combine like terms: 8x + -8x = 0 -700 + -8x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -700 + -8x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -700 + -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'. -142.8571429 + -1.632653061x + x2 = 0 Move the constant term to the right: Add '142.8571429' to each side of the equation. -142.8571429 + -1.632653061x + 142.8571429 + x2 = 0 + 142.8571429 Reorder the terms: -142.8571429 + 142.8571429 + -1.632653061x + x2 = 0 + 142.8571429 Combine like terms: -142.8571429 + 142.8571429 = 0.0000000 0.0000000 + -1.632653061x + x2 = 0 + 142.8571429 -1.632653061x + x2 = 0 + 142.8571429 Combine like terms: 0 + 142.8571429 = 142.8571429 -1.632653061x + x2 = 142.8571429 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 = 142.8571429 + 0.6663890044 Reorder the terms: 0.6663890044 + -1.632653061x + x2 = 142.8571429 + 0.6663890044 Combine like terms: 142.8571429 + 0.6663890044 = 143.5235319044 0.6663890044 + -1.632653061x + x2 = 143.5235319044 Factor a perfect square on the left side: (x + -0.8163265305)(x + -0.8163265305) = 143.5235319044 Calculate the square root of the right side: 11.980130713 Break this problem into two subproblems by setting (x + -0.8163265305) equal to 11.980130713 and -11.980130713.Subproblem 1
x + -0.8163265305 = 11.980130713 Simplifying x + -0.8163265305 = 11.980130713 Reorder the terms: -0.8163265305 + x = 11.980130713 Solving -0.8163265305 + x = 11.980130713 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 = 11.980130713 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = 11.980130713 + 0.8163265305 x = 11.980130713 + 0.8163265305 Combine like terms: 11.980130713 + 0.8163265305 = 12.7964572435 x = 12.7964572435 Simplifying x = 12.7964572435Subproblem 2
x + -0.8163265305 = -11.980130713 Simplifying x + -0.8163265305 = -11.980130713 Reorder the terms: -0.8163265305 + x = -11.980130713 Solving -0.8163265305 + x = -11.980130713 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 = -11.980130713 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = -11.980130713 + 0.8163265305 x = -11.980130713 + 0.8163265305 Combine like terms: -11.980130713 + 0.8163265305 = -11.1638041825 x = -11.1638041825 Simplifying x = -11.1638041825Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.7964572435, -11.1638041825}
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