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Simplifying 0.01x2 + 0.22x + 8.30 = 9.5 Reorder the terms: 8.30 + 0.22x + 0.01x2 = 9.5 Solving 8.30 + 0.22x + 0.01x2 = 9.5 Solving for variable 'x'. Reorder the terms: 8.30 + -9.5 + 0.22x + 0.01x2 = 9.5 + -9.5 Combine like terms: 8.30 + -9.5 = -1.2 -1.2 + 0.22x + 0.01x2 = 9.5 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 -1.2 + 0.22x + 0.01x2 = 0.0 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -120 + 22x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 22x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 22x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 22x + x2 = 0 + 120 22x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 22x + x2 = 120 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 120 + 121 Reorder the terms: 121 + 22x + x2 = 120 + 121 Combine like terms: 120 + 121 = 241 121 + 22x + x2 = 241 Factor a perfect square on the left side: (x + 11)(x + 11) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (x + 11) equal to 15.524174696 and -15.524174696.Subproblem 1
x + 11 = 15.524174696 Simplifying x + 11 = 15.524174696 Reorder the terms: 11 + x = 15.524174696 Solving 11 + x = 15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 15.524174696 + -11 Combine like terms: 11 + -11 = 0 0 + x = 15.524174696 + -11 x = 15.524174696 + -11 Combine like terms: 15.524174696 + -11 = 4.524174696 x = 4.524174696 Simplifying x = 4.524174696Subproblem 2
x + 11 = -15.524174696 Simplifying x + 11 = -15.524174696 Reorder the terms: 11 + x = -15.524174696 Solving 11 + x = -15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -15.524174696 + -11 Combine like terms: 11 + -11 = 0 0 + x = -15.524174696 + -11 x = -15.524174696 + -11 Combine like terms: -15.524174696 + -11 = -26.524174696 x = -26.524174696 Simplifying x = -26.524174696Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.524174696, -26.524174696}
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