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Simplifying 0.3x2 + -11.1x + 85.8 = 0 Reorder the terms: 85.8 + -11.1x + 0.3x2 = 0 Solving 85.8 + -11.1x + 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'. 286 + -37x + x2 = 0 Move the constant term to the right: Add '-286' to each side of the equation. 286 + -37x + -286 + x2 = 0 + -286 Reorder the terms: 286 + -286 + -37x + x2 = 0 + -286 Combine like terms: 286 + -286 = 0 0 + -37x + x2 = 0 + -286 -37x + x2 = 0 + -286 Combine like terms: 0 + -286 = -286 -37x + x2 = -286 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = -286 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -286 + 342.25 Combine like terms: -286 + 342.25 = 56.25 342.25 + -37x + x2 = 56.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 56.25 Calculate the square root of the right side: 7.5 Break this problem into two subproblems by setting (x + -18.5) equal to 7.5 and -7.5.Subproblem 1
x + -18.5 = 7.5 Simplifying x + -18.5 = 7.5 Reorder the terms: -18.5 + x = 7.5 Solving -18.5 + x = 7.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 7.5 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 7.5 + 18.5 x = 7.5 + 18.5 Combine like terms: 7.5 + 18.5 = 26 x = 26 Simplifying x = 26Subproblem 2
x + -18.5 = -7.5 Simplifying x + -18.5 = -7.5 Reorder the terms: -18.5 + x = -7.5 Solving -18.5 + x = -7.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -7.5 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -7.5 + 18.5 x = -7.5 + 18.5 Combine like terms: -7.5 + 18.5 = 11 x = 11 Simplifying x = 11Solution
The solution to the problem is based on the solutions from the subproblems. x = {26, 11}
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