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Simplifying 0.3x2 + -8.1x + 0.9 = 0 Reorder the terms: 0.9 + -8.1x + 0.3x2 = 0 Solving 0.9 + -8.1x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 3 + -27x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -27x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -27x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -27x + x2 = 0 + -3 -27x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -27x + x2 = -3 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = -3 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -3 + 182.25 Combine like terms: -3 + 182.25 = 179.25 182.25 + -27x + x2 = 179.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 179.25 Calculate the square root of the right side: 13.388427839 Break this problem into two subproblems by setting (x + -13.5) equal to 13.388427839 and -13.388427839.Subproblem 1
x + -13.5 = 13.388427839 Simplifying x + -13.5 = 13.388427839 Reorder the terms: -13.5 + x = 13.388427839 Solving -13.5 + x = 13.388427839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 13.388427839 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 13.388427839 + 13.5 x = 13.388427839 + 13.5 Combine like terms: 13.388427839 + 13.5 = 26.888427839 x = 26.888427839 Simplifying x = 26.888427839Subproblem 2
x + -13.5 = -13.388427839 Simplifying x + -13.5 = -13.388427839 Reorder the terms: -13.5 + x = -13.388427839 Solving -13.5 + x = -13.388427839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -13.388427839 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -13.388427839 + 13.5 x = -13.388427839 + 13.5 Combine like terms: -13.388427839 + 13.5 = 0.111572161 x = 0.111572161 Simplifying x = 0.111572161Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.888427839, 0.111572161}
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