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Simplifying 0.6679 = -0.0074x2 + 0.2505x Reorder the terms: 0.6679 = 0.2505x + -0.0074x2 Solving 0.6679 = 0.2505x + -0.0074x2 Solving for variable 'x'. Reorder the terms: 0.6679 + -0.2505x + 0.0074x2 = 0.2505x + -0.2505x + -0.0074x2 + 0.0074x2 Combine like terms: 0.2505x + -0.2505x = 0.0000 0.6679 + -0.2505x + 0.0074x2 = 0.0000 + -0.0074x2 + 0.0074x2 0.6679 + -0.2505x + 0.0074x2 = -0.0074x2 + 0.0074x2 Combine like terms: -0.0074x2 + 0.0074x2 = 0.0000 0.6679 + -0.2505x + 0.0074x2 = 0.0000 Begin completing the square. Divide all terms by 0.0074 the coefficient of the squared term: Divide each side by '0.0074'. 90.25675676 + -33.85135135x + x2 = 0 Move the constant term to the right: Add '-90.25675676' to each side of the equation. 90.25675676 + -33.85135135x + -90.25675676 + x2 = 0 + -90.25675676 Reorder the terms: 90.25675676 + -90.25675676 + -33.85135135x + x2 = 0 + -90.25675676 Combine like terms: 90.25675676 + -90.25675676 = 0.00000000 0.00000000 + -33.85135135x + x2 = 0 + -90.25675676 -33.85135135x + x2 = 0 + -90.25675676 Combine like terms: 0 + -90.25675676 = -90.25675676 -33.85135135x + x2 = -90.25675676 The x term is -33.85135135x. Take half its coefficient (-16.92567568). Square it (286.4784972) and add it to both sides. Add '286.4784972' to each side of the equation. -33.85135135x + 286.4784972 + x2 = -90.25675676 + 286.4784972 Reorder the terms: 286.4784972 + -33.85135135x + x2 = -90.25675676 + 286.4784972 Combine like terms: -90.25675676 + 286.4784972 = 196.22174044 286.4784972 + -33.85135135x + x2 = 196.22174044 Factor a perfect square on the left side: (x + -16.92567568)(x + -16.92567568) = 196.22174044 Calculate the square root of the right side: 14.007917063 Break this problem into two subproblems by setting (x + -16.92567568) equal to 14.007917063 and -14.007917063.Subproblem 1
x + -16.92567568 = 14.007917063 Simplifying x + -16.92567568 = 14.007917063 Reorder the terms: -16.92567568 + x = 14.007917063 Solving -16.92567568 + x = 14.007917063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.92567568' to each side of the equation. -16.92567568 + 16.92567568 + x = 14.007917063 + 16.92567568 Combine like terms: -16.92567568 + 16.92567568 = 0.00000000 0.00000000 + x = 14.007917063 + 16.92567568 x = 14.007917063 + 16.92567568 Combine like terms: 14.007917063 + 16.92567568 = 30.933592743 x = 30.933592743 Simplifying x = 30.933592743Subproblem 2
x + -16.92567568 = -14.007917063 Simplifying x + -16.92567568 = -14.007917063 Reorder the terms: -16.92567568 + x = -14.007917063 Solving -16.92567568 + x = -14.007917063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.92567568' to each side of the equation. -16.92567568 + 16.92567568 + x = -14.007917063 + 16.92567568 Combine like terms: -16.92567568 + 16.92567568 = 0.00000000 0.00000000 + x = -14.007917063 + 16.92567568 x = -14.007917063 + 16.92567568 Combine like terms: -14.007917063 + 16.92567568 = 2.917758617 x = 2.917758617 Simplifying x = 2.917758617Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.933592743, 2.917758617}
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