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Simplifying -0.021x2 + 2.6x + 35 = 0 Reorder the terms: 35 + 2.6x + -0.021x2 = 0 Solving 35 + 2.6x + -0.021x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.021 the coefficient of the squared term: Divide each side by '-0.021'. -1666.666667 + -123.8095238x + x2 = 0 Move the constant term to the right: Add '1666.666667' to each side of the equation. -1666.666667 + -123.8095238x + 1666.666667 + x2 = 0 + 1666.666667 Reorder the terms: -1666.666667 + 1666.666667 + -123.8095238x + x2 = 0 + 1666.666667 Combine like terms: -1666.666667 + 1666.666667 = 0.000000 0.000000 + -123.8095238x + x2 = 0 + 1666.666667 -123.8095238x + x2 = 0 + 1666.666667 Combine like terms: 0 + 1666.666667 = 1666.666667 -123.8095238x + x2 = 1666.666667 The x term is -123.8095238x. Take half its coefficient (-61.9047619). Square it (3832.199546) and add it to both sides. Add '3832.199546' to each side of the equation. -123.8095238x + 3832.199546 + x2 = 1666.666667 + 3832.199546 Reorder the terms: 3832.199546 + -123.8095238x + x2 = 1666.666667 + 3832.199546 Combine like terms: 1666.666667 + 3832.199546 = 5498.866213 3832.199546 + -123.8095238x + x2 = 5498.866213 Factor a perfect square on the left side: (x + -61.9047619)(x + -61.9047619) = 5498.866213 Calculate the square root of the right side: 74.154340487 Break this problem into two subproblems by setting (x + -61.9047619) equal to 74.154340487 and -74.154340487.Subproblem 1
x + -61.9047619 = 74.154340487 Simplifying x + -61.9047619 = 74.154340487 Reorder the terms: -61.9047619 + x = 74.154340487 Solving -61.9047619 + x = 74.154340487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '61.9047619' to each side of the equation. -61.9047619 + 61.9047619 + x = 74.154340487 + 61.9047619 Combine like terms: -61.9047619 + 61.9047619 = 0.0000000 0.0000000 + x = 74.154340487 + 61.9047619 x = 74.154340487 + 61.9047619 Combine like terms: 74.154340487 + 61.9047619 = 136.059102387 x = 136.059102387 Simplifying x = 136.059102387Subproblem 2
x + -61.9047619 = -74.154340487 Simplifying x + -61.9047619 = -74.154340487 Reorder the terms: -61.9047619 + x = -74.154340487 Solving -61.9047619 + x = -74.154340487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '61.9047619' to each side of the equation. -61.9047619 + 61.9047619 + x = -74.154340487 + 61.9047619 Combine like terms: -61.9047619 + 61.9047619 = 0.0000000 0.0000000 + x = -74.154340487 + 61.9047619 x = -74.154340487 + 61.9047619 Combine like terms: -74.154340487 + 61.9047619 = -12.249578587 x = -12.249578587 Simplifying x = -12.249578587Solution
The solution to the problem is based on the solutions from the subproblems. x = {136.059102387, -12.249578587}
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