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Simplifying 18x2 + -7x + -5 = 0 Reorder the terms: -5 + -7x + 18x2 = 0 Solving -5 + -7x + 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'. -0.2777777778 + -0.3888888889x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + -0.3888888889x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + -0.3888888889x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + -0.3888888889x + x2 = 0 + 0.2777777778 -0.3888888889x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 -0.3888888889x + x2 = 0.2777777778 The x term is -0.3888888889x. Take half its coefficient (-0.1944444445). Square it (0.03780864200) and add it to both sides. Add '0.03780864200' to each side of the equation. -0.3888888889x + 0.03780864200 + x2 = 0.2777777778 + 0.03780864200 Reorder the terms: 0.03780864200 + -0.3888888889x + x2 = 0.2777777778 + 0.03780864200 Combine like terms: 0.2777777778 + 0.03780864200 = 0.3155864198 0.03780864200 + -0.3888888889x + x2 = 0.3155864198 Factor a perfect square on the left side: (x + -0.1944444445)(x + -0.1944444445) = 0.3155864198 Calculate the square root of the right side: 0.561770789 Break this problem into two subproblems by setting (x + -0.1944444445) equal to 0.561770789 and -0.561770789.Subproblem 1
x + -0.1944444445 = 0.561770789 Simplifying x + -0.1944444445 = 0.561770789 Reorder the terms: -0.1944444445 + x = 0.561770789 Solving -0.1944444445 + x = 0.561770789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1944444445' to each side of the equation. -0.1944444445 + 0.1944444445 + x = 0.561770789 + 0.1944444445 Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000 0.0000000000 + x = 0.561770789 + 0.1944444445 x = 0.561770789 + 0.1944444445 Combine like terms: 0.561770789 + 0.1944444445 = 0.7562152335 x = 0.7562152335 Simplifying x = 0.7562152335Subproblem 2
x + -0.1944444445 = -0.561770789 Simplifying x + -0.1944444445 = -0.561770789 Reorder the terms: -0.1944444445 + x = -0.561770789 Solving -0.1944444445 + x = -0.561770789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1944444445' to each side of the equation. -0.1944444445 + 0.1944444445 + x = -0.561770789 + 0.1944444445 Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000 0.0000000000 + x = -0.561770789 + 0.1944444445 x = -0.561770789 + 0.1944444445 Combine like terms: -0.561770789 + 0.1944444445 = -0.3673263445 x = -0.3673263445 Simplifying x = -0.3673263445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7562152335, -0.3673263445}
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