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Simplifying -0.01x2 + 0.22x + 8.20 = 0 Reorder the terms: 8.20 + 0.22x + -0.01x2 = 0 Solving 8.20 + 0.22x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -820 + -22x + x2 = 0 Move the constant term to the right: Add '820' to each side of the equation. -820 + -22x + 820 + x2 = 0 + 820 Reorder the terms: -820 + 820 + -22x + x2 = 0 + 820 Combine like terms: -820 + 820 = 0 0 + -22x + x2 = 0 + 820 -22x + x2 = 0 + 820 Combine like terms: 0 + 820 = 820 -22x + x2 = 820 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 = 820 + 121 Reorder the terms: 121 + -22x + x2 = 820 + 121 Combine like terms: 820 + 121 = 941 121 + -22x + x2 = 941 Factor a perfect square on the left side: (x + -11)(x + -11) = 941 Calculate the square root of the right side: 30.6757233 Break this problem into two subproblems by setting (x + -11) equal to 30.6757233 and -30.6757233.Subproblem 1
x + -11 = 30.6757233 Simplifying x + -11 = 30.6757233 Reorder the terms: -11 + x = 30.6757233 Solving -11 + x = 30.6757233 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 = 30.6757233 + 11 Combine like terms: -11 + 11 = 0 0 + x = 30.6757233 + 11 x = 30.6757233 + 11 Combine like terms: 30.6757233 + 11 = 41.6757233 x = 41.6757233 Simplifying x = 41.6757233Subproblem 2
x + -11 = -30.6757233 Simplifying x + -11 = -30.6757233 Reorder the terms: -11 + x = -30.6757233 Solving -11 + x = -30.6757233 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 = -30.6757233 + 11 Combine like terms: -11 + 11 = 0 0 + x = -30.6757233 + 11 x = -30.6757233 + 11 Combine like terms: -30.6757233 + 11 = -19.6757233 x = -19.6757233 Simplifying x = -19.6757233Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.6757233, -19.6757233}
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