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Simplifying 0.11111111111x2 + -13x + 324 = 0 Reorder the terms: 324 + -13x + 0.11111111111x2 = 0 Solving 324 + -13x + 0.11111111111x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.11111111111 the coefficient of the squared term: Divide each side by '0.11111111111'. 2916 + -117x + x2 = 0 Move the constant term to the right: Add '-2916' to each side of the equation. 2916 + -117x + -2916 + x2 = 0 + -2916 Reorder the terms: 2916 + -2916 + -117x + x2 = 0 + -2916 Combine like terms: 2916 + -2916 = 0 0 + -117x + x2 = 0 + -2916 -117x + x2 = 0 + -2916 Combine like terms: 0 + -2916 = -2916 -117x + x2 = -2916 The x term is -117x. Take half its coefficient (-58.5). Square it (3422.25) and add it to both sides. Add '3422.25' to each side of the equation. -117x + 3422.25 + x2 = -2916 + 3422.25 Reorder the terms: 3422.25 + -117x + x2 = -2916 + 3422.25 Combine like terms: -2916 + 3422.25 = 506.25 3422.25 + -117x + x2 = 506.25 Factor a perfect square on the left side: (x + -58.5)(x + -58.5) = 506.25 Calculate the square root of the right side: 22.5 Break this problem into two subproblems by setting (x + -58.5) equal to 22.5 and -22.5.Subproblem 1
x + -58.5 = 22.5 Simplifying x + -58.5 = 22.5 Reorder the terms: -58.5 + x = 22.5 Solving -58.5 + x = 22.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58.5' to each side of the equation. -58.5 + 58.5 + x = 22.5 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + x = 22.5 + 58.5 x = 22.5 + 58.5 Combine like terms: 22.5 + 58.5 = 81 x = 81 Simplifying x = 81Subproblem 2
x + -58.5 = -22.5 Simplifying x + -58.5 = -22.5 Reorder the terms: -58.5 + x = -22.5 Solving -58.5 + x = -22.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58.5' to each side of the equation. -58.5 + 58.5 + x = -22.5 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + x = -22.5 + 58.5 x = -22.5 + 58.5 Combine like terms: -22.5 + 58.5 = 36 x = 36 Simplifying x = 36Solution
The solution to the problem is based on the solutions from the subproblems. x = {81, 36}
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