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Simplifying 90 = -0.4931x2 + 11.077x + 34.805 Reorder the terms: 90 = 34.805 + 11.077x + -0.4931x2 Solving 90 = 34.805 + 11.077x + -0.4931x2 Solving for variable 'x'. Combine like terms: 90 + -34.805 = 55.195 55.195 + -11.077x + 0.4931x2 = 34.805 + 11.077x + -0.4931x2 + -34.805 + -11.077x + 0.4931x2 Reorder the terms: 55.195 + -11.077x + 0.4931x2 = 34.805 + -34.805 + 11.077x + -11.077x + -0.4931x2 + 0.4931x2 Combine like terms: 34.805 + -34.805 = 0.000 55.195 + -11.077x + 0.4931x2 = 0.000 + 11.077x + -11.077x + -0.4931x2 + 0.4931x2 55.195 + -11.077x + 0.4931x2 = 11.077x + -11.077x + -0.4931x2 + 0.4931x2 Combine like terms: 11.077x + -11.077x = 0.000 55.195 + -11.077x + 0.4931x2 = 0.000 + -0.4931x2 + 0.4931x2 55.195 + -11.077x + 0.4931x2 = -0.4931x2 + 0.4931x2 Combine like terms: -0.4931x2 + 0.4931x2 = 0.0000 55.195 + -11.077x + 0.4931x2 = 0.0000 Begin completing the square. Divide all terms by 0.4931 the coefficient of the squared term: Divide each side by '0.4931'. 111.9346988 + -22.46400324x + x2 = 0 Move the constant term to the right: Add '-111.9346988' to each side of the equation. 111.9346988 + -22.46400324x + -111.9346988 + x2 = 0 + -111.9346988 Reorder the terms: 111.9346988 + -111.9346988 + -22.46400324x + x2 = 0 + -111.9346988 Combine like terms: 111.9346988 + -111.9346988 = 0.0000000 0.0000000 + -22.46400324x + x2 = 0 + -111.9346988 -22.46400324x + x2 = 0 + -111.9346988 Combine like terms: 0 + -111.9346988 = -111.9346988 -22.46400324x + x2 = -111.9346988 The x term is -22.46400324x. Take half its coefficient (-11.23200162). Square it (126.1578604) and add it to both sides. Add '126.1578604' to each side of the equation. -22.46400324x + 126.1578604 + x2 = -111.9346988 + 126.1578604 Reorder the terms: 126.1578604 + -22.46400324x + x2 = -111.9346988 + 126.1578604 Combine like terms: -111.9346988 + 126.1578604 = 14.2231616 126.1578604 + -22.46400324x + x2 = 14.2231616 Factor a perfect square on the left side: (x + -11.23200162)(x + -11.23200162) = 14.2231616 Calculate the square root of the right side: 3.771360709 Break this problem into two subproblems by setting (x + -11.23200162) equal to 3.771360709 and -3.771360709.Subproblem 1
x + -11.23200162 = 3.771360709 Simplifying x + -11.23200162 = 3.771360709 Reorder the terms: -11.23200162 + x = 3.771360709 Solving -11.23200162 + x = 3.771360709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.23200162' to each side of the equation. -11.23200162 + 11.23200162 + x = 3.771360709 + 11.23200162 Combine like terms: -11.23200162 + 11.23200162 = 0.00000000 0.00000000 + x = 3.771360709 + 11.23200162 x = 3.771360709 + 11.23200162 Combine like terms: 3.771360709 + 11.23200162 = 15.003362329 x = 15.003362329 Simplifying x = 15.003362329Subproblem 2
x + -11.23200162 = -3.771360709 Simplifying x + -11.23200162 = -3.771360709 Reorder the terms: -11.23200162 + x = -3.771360709 Solving -11.23200162 + x = -3.771360709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.23200162' to each side of the equation. -11.23200162 + 11.23200162 + x = -3.771360709 + 11.23200162 Combine like terms: -11.23200162 + 11.23200162 = 0.00000000 0.00000000 + x = -3.771360709 + 11.23200162 x = -3.771360709 + 11.23200162 Combine like terms: -3.771360709 + 11.23200162 = 7.460640911 x = 7.460640911 Simplifying x = 7.460640911Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.003362329, 7.460640911}
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