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Simplifying 9x2 + -17x + -18 = 0 Reorder the terms: -18 + -17x + 9x2 = 0 Solving -18 + -17x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.888888889x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -1.888888889x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.888888889x + x2 = 0 + 2 -1.888888889x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.888888889x + x2 = 2 The x term is -1.888888889x. Take half its coefficient (-0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. -1.888888889x + 0.8919753087 + x2 = 2 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = 2 + 0.8919753087 Combine like terms: 2 + 0.8919753087 = 2.8919753087 0.8919753087 + -1.888888889x + x2 = 2.8919753087 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 2.8919753087 Calculate the square root of the right side: 1.700580874 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 1.700580874 and -1.700580874.Subproblem 1
x + -0.9444444445 = 1.700580874 Simplifying x + -0.9444444445 = 1.700580874 Reorder the terms: -0.9444444445 + x = 1.700580874 Solving -0.9444444445 + x = 1.700580874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = 1.700580874 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 1.700580874 + 0.9444444445 x = 1.700580874 + 0.9444444445 Combine like terms: 1.700580874 + 0.9444444445 = 2.6450253185 x = 2.6450253185 Simplifying x = 2.6450253185Subproblem 2
x + -0.9444444445 = -1.700580874 Simplifying x + -0.9444444445 = -1.700580874 Reorder the terms: -0.9444444445 + x = -1.700580874 Solving -0.9444444445 + x = -1.700580874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = -1.700580874 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -1.700580874 + 0.9444444445 x = -1.700580874 + 0.9444444445 Combine like terms: -1.700580874 + 0.9444444445 = -0.7561364295 x = -0.7561364295 Simplifying x = -0.7561364295Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6450253185, -0.7561364295}
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