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Simplifying 18x2 + -7x + -9 = 0 Reorder the terms: -9 + -7x + 18x2 = 0 Solving -9 + -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'. -0.5 + -0.3888888889x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.3888888889x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.3888888889x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.3888888889x + x2 = 0 + 0.5 -0.3888888889x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.3888888889x + x2 = 0.5 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 = 0.5 + 0.03780864200 Reorder the terms: 0.03780864200 + -0.3888888889x + x2 = 0.5 + 0.03780864200 Combine like terms: 0.5 + 0.03780864200 = 0.537808642 0.03780864200 + -0.3888888889x + x2 = 0.537808642 Factor a perfect square on the left side: (x + -0.1944444445)(x + -0.1944444445) = 0.537808642 Calculate the square root of the right side: 0.733354377 Break this problem into two subproblems by setting (x + -0.1944444445) equal to 0.733354377 and -0.733354377.Subproblem 1
x + -0.1944444445 = 0.733354377 Simplifying x + -0.1944444445 = 0.733354377 Reorder the terms: -0.1944444445 + x = 0.733354377 Solving -0.1944444445 + x = 0.733354377 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 = 0.733354377 + 0.1944444445 Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000 0.0000000000 + x = 0.733354377 + 0.1944444445 x = 0.733354377 + 0.1944444445 Combine like terms: 0.733354377 + 0.1944444445 = 0.9277988215 x = 0.9277988215 Simplifying x = 0.9277988215Subproblem 2
x + -0.1944444445 = -0.733354377 Simplifying x + -0.1944444445 = -0.733354377 Reorder the terms: -0.1944444445 + x = -0.733354377 Solving -0.1944444445 + x = -0.733354377 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 = -0.733354377 + 0.1944444445 Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000 0.0000000000 + x = -0.733354377 + 0.1944444445 x = -0.733354377 + 0.1944444445 Combine like terms: -0.733354377 + 0.1944444445 = -0.5389099325 x = -0.5389099325 Simplifying x = -0.5389099325Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9277988215, -0.5389099325}
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