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Simplifying 80 = -0.27x2 + 3.3x + 77 Reorder the terms: 80 = 77 + 3.3x + -0.27x2 Solving 80 = 77 + 3.3x + -0.27x2 Solving for variable 'x'. Combine like terms: 80 + -77 = 3 3 + -3.3x + 0.27x2 = 77 + 3.3x + -0.27x2 + -77 + -3.3x + 0.27x2 Reorder the terms: 3 + -3.3x + 0.27x2 = 77 + -77 + 3.3x + -3.3x + -0.27x2 + 0.27x2 Combine like terms: 77 + -77 = 0 3 + -3.3x + 0.27x2 = 0 + 3.3x + -3.3x + -0.27x2 + 0.27x2 3 + -3.3x + 0.27x2 = 3.3x + -3.3x + -0.27x2 + 0.27x2 Combine like terms: 3.3x + -3.3x = 0.0 3 + -3.3x + 0.27x2 = 0.0 + -0.27x2 + 0.27x2 3 + -3.3x + 0.27x2 = -0.27x2 + 0.27x2 Combine like terms: -0.27x2 + 0.27x2 = 0.00 3 + -3.3x + 0.27x2 = 0.00 Begin completing the square. Divide all terms by 0.27 the coefficient of the squared term: Divide each side by '0.27'. 11.11111111 + -12.22222222x + x2 = 0 Move the constant term to the right: Add '-11.11111111' to each side of the equation. 11.11111111 + -12.22222222x + -11.11111111 + x2 = 0 + -11.11111111 Reorder the terms: 11.11111111 + -11.11111111 + -12.22222222x + x2 = 0 + -11.11111111 Combine like terms: 11.11111111 + -11.11111111 = 0.00000000 0.00000000 + -12.22222222x + x2 = 0 + -11.11111111 -12.22222222x + x2 = 0 + -11.11111111 Combine like terms: 0 + -11.11111111 = -11.11111111 -12.22222222x + x2 = -11.11111111 The x term is -12.22222222x. Take half its coefficient (-6.11111111). Square it (37.34567900) and add it to both sides. Add '37.34567900' to each side of the equation. -12.22222222x + 37.34567900 + x2 = -11.11111111 + 37.34567900 Reorder the terms: 37.34567900 + -12.22222222x + x2 = -11.11111111 + 37.34567900 Combine like terms: -11.11111111 + 37.34567900 = 26.23456789 37.34567900 + -12.22222222x + x2 = 26.23456789 Factor a perfect square on the left side: (x + -6.11111111)(x + -6.11111111) = 26.23456789 Calculate the square root of the right side: 5.121969142 Break this problem into two subproblems by setting (x + -6.11111111) equal to 5.121969142 and -5.121969142.Subproblem 1
x + -6.11111111 = 5.121969142 Simplifying x + -6.11111111 = 5.121969142 Reorder the terms: -6.11111111 + x = 5.121969142 Solving -6.11111111 + x = 5.121969142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.11111111' to each side of the equation. -6.11111111 + 6.11111111 + x = 5.121969142 + 6.11111111 Combine like terms: -6.11111111 + 6.11111111 = 0.00000000 0.00000000 + x = 5.121969142 + 6.11111111 x = 5.121969142 + 6.11111111 Combine like terms: 5.121969142 + 6.11111111 = 11.233080252 x = 11.233080252 Simplifying x = 11.233080252Subproblem 2
x + -6.11111111 = -5.121969142 Simplifying x + -6.11111111 = -5.121969142 Reorder the terms: -6.11111111 + x = -5.121969142 Solving -6.11111111 + x = -5.121969142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.11111111' to each side of the equation. -6.11111111 + 6.11111111 + x = -5.121969142 + 6.11111111 Combine like terms: -6.11111111 + 6.11111111 = 0.00000000 0.00000000 + x = -5.121969142 + 6.11111111 x = -5.121969142 + 6.11111111 Combine like terms: -5.121969142 + 6.11111111 = 0.989141968 x = 0.989141968 Simplifying x = 0.989141968Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.233080252, 0.989141968}
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