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Simplifying 18x2 + -18x + -49 = 0 Reorder the terms: -49 + -18x + 18x2 = 0 Solving -49 + -18x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -2.722222222 + -1x + x2 = 0 Move the constant term to the right: Add '2.722222222' to each side of the equation. -2.722222222 + -1x + 2.722222222 + x2 = 0 + 2.722222222 Reorder the terms: -2.722222222 + 2.722222222 + -1x + x2 = 0 + 2.722222222 Combine like terms: -2.722222222 + 2.722222222 = 0.000000000 0.000000000 + -1x + x2 = 0 + 2.722222222 -1x + x2 = 0 + 2.722222222 Combine like terms: 0 + 2.722222222 = 2.722222222 -1x + x2 = 2.722222222 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.722222222 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.722222222 + 0.25 Combine like terms: 2.722222222 + 0.25 = 2.972222222 0.25 + -1x + x2 = 2.972222222 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.972222222 Calculate the square root of the right side: 1.724013405 Break this problem into two subproblems by setting (x + -0.5) equal to 1.724013405 and -1.724013405.Subproblem 1
x + -0.5 = 1.724013405 Simplifying x + -0.5 = 1.724013405 Reorder the terms: -0.5 + x = 1.724013405 Solving -0.5 + x = 1.724013405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.724013405 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.724013405 + 0.5 x = 1.724013405 + 0.5 Combine like terms: 1.724013405 + 0.5 = 2.224013405 x = 2.224013405 Simplifying x = 2.224013405Subproblem 2
x + -0.5 = -1.724013405 Simplifying x + -0.5 = -1.724013405 Reorder the terms: -0.5 + x = -1.724013405 Solving -0.5 + x = -1.724013405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.724013405 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.724013405 + 0.5 x = -1.724013405 + 0.5 Combine like terms: -1.724013405 + 0.5 = -1.224013405 x = -1.224013405 Simplifying x = -1.224013405Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.224013405, -1.224013405}
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