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Simplifying -0.017x2 + 0.98x + 0.33 = 10 Reorder the terms: 0.33 + 0.98x + -0.017x2 = 10 Solving 0.33 + 0.98x + -0.017x2 = 10 Solving for variable 'x'. Reorder the terms: 0.33 + -10 + 0.98x + -0.017x2 = 10 + -10 Combine like terms: 0.33 + -10 = -9.67 -9.67 + 0.98x + -0.017x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -9.67 + 0.98x + -0.017x2 = 0 Begin completing the square. Divide all terms by -0.017 the coefficient of the squared term: Divide each side by '-0.017'. 568.8235294 + -57.64705882x + x2 = 0 Move the constant term to the right: Add '-568.8235294' to each side of the equation. 568.8235294 + -57.64705882x + -568.8235294 + x2 = 0 + -568.8235294 Reorder the terms: 568.8235294 + -568.8235294 + -57.64705882x + x2 = 0 + -568.8235294 Combine like terms: 568.8235294 + -568.8235294 = 0.0000000 0.0000000 + -57.64705882x + x2 = 0 + -568.8235294 -57.64705882x + x2 = 0 + -568.8235294 Combine like terms: 0 + -568.8235294 = -568.8235294 -57.64705882x + x2 = -568.8235294 The x term is -57.64705882x. Take half its coefficient (-28.82352941). Square it (830.7958476) and add it to both sides. Add '830.7958476' to each side of the equation. -57.64705882x + 830.7958476 + x2 = -568.8235294 + 830.7958476 Reorder the terms: 830.7958476 + -57.64705882x + x2 = -568.8235294 + 830.7958476 Combine like terms: -568.8235294 + 830.7958476 = 261.9723182 830.7958476 + -57.64705882x + x2 = 261.9723182 Factor a perfect square on the left side: (x + -28.82352941)(x + -28.82352941) = 261.9723182 Calculate the square root of the right side: 16.18555894 Break this problem into two subproblems by setting (x + -28.82352941) equal to 16.18555894 and -16.18555894.Subproblem 1
x + -28.82352941 = 16.18555894 Simplifying x + -28.82352941 = 16.18555894 Reorder the terms: -28.82352941 + x = 16.18555894 Solving -28.82352941 + x = 16.18555894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.82352941' to each side of the equation. -28.82352941 + 28.82352941 + x = 16.18555894 + 28.82352941 Combine like terms: -28.82352941 + 28.82352941 = 0.00000000 0.00000000 + x = 16.18555894 + 28.82352941 x = 16.18555894 + 28.82352941 Combine like terms: 16.18555894 + 28.82352941 = 45.00908835 x = 45.00908835 Simplifying x = 45.00908835Subproblem 2
x + -28.82352941 = -16.18555894 Simplifying x + -28.82352941 = -16.18555894 Reorder the terms: -28.82352941 + x = -16.18555894 Solving -28.82352941 + x = -16.18555894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.82352941' to each side of the equation. -28.82352941 + 28.82352941 + x = -16.18555894 + 28.82352941 Combine like terms: -28.82352941 + 28.82352941 = 0.00000000 0.00000000 + x = -16.18555894 + 28.82352941 x = -16.18555894 + 28.82352941 Combine like terms: -16.18555894 + 28.82352941 = 12.63797047 x = 12.63797047 Simplifying x = 12.63797047Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.00908835, 12.63797047}
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