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Simplifying -4.9x2 + -6x + 800 = 0 Reorder the terms: 800 + -6x + -4.9x2 = 0 Solving 800 + -6x + -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'. -163.2653061 + 1.224489796x + x2 = 0 Move the constant term to the right: Add '163.2653061' to each side of the equation. -163.2653061 + 1.224489796x + 163.2653061 + x2 = 0 + 163.2653061 Reorder the terms: -163.2653061 + 163.2653061 + 1.224489796x + x2 = 0 + 163.2653061 Combine like terms: -163.2653061 + 163.2653061 = 0.0000000 0.0000000 + 1.224489796x + x2 = 0 + 163.2653061 1.224489796x + x2 = 0 + 163.2653061 Combine like terms: 0 + 163.2653061 = 163.2653061 1.224489796x + x2 = 163.2653061 The x term is 1.224489796x. Take half its coefficient (0.612244898). Square it (0.3748438151) and add it to both sides. Add '0.3748438151' to each side of the equation. 1.224489796x + 0.3748438151 + x2 = 163.2653061 + 0.3748438151 Reorder the terms: 0.3748438151 + 1.224489796x + x2 = 163.2653061 + 0.3748438151 Combine like terms: 163.2653061 + 0.3748438151 = 163.6401499151 0.3748438151 + 1.224489796x + x2 = 163.6401499151 Factor a perfect square on the left side: (x + 0.612244898)(x + 0.612244898) = 163.6401499151 Calculate the square root of the right side: 12.792190974 Break this problem into two subproblems by setting (x + 0.612244898) equal to 12.792190974 and -12.792190974.Subproblem 1
x + 0.612244898 = 12.792190974 Simplifying x + 0.612244898 = 12.792190974 Reorder the terms: 0.612244898 + x = 12.792190974 Solving 0.612244898 + x = 12.792190974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.612244898' to each side of the equation. 0.612244898 + -0.612244898 + x = 12.792190974 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + x = 12.792190974 + -0.612244898 x = 12.792190974 + -0.612244898 Combine like terms: 12.792190974 + -0.612244898 = 12.179946076 x = 12.179946076 Simplifying x = 12.179946076Subproblem 2
x + 0.612244898 = -12.792190974 Simplifying x + 0.612244898 = -12.792190974 Reorder the terms: 0.612244898 + x = -12.792190974 Solving 0.612244898 + x = -12.792190974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.612244898' to each side of the equation. 0.612244898 + -0.612244898 + x = -12.792190974 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + x = -12.792190974 + -0.612244898 x = -12.792190974 + -0.612244898 Combine like terms: -12.792190974 + -0.612244898 = -13.404435872 x = -13.404435872 Simplifying x = -13.404435872Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.179946076, -13.404435872}
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