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Simplifying 9x2 + -17x + -116 = 0 Reorder the terms: -116 + -17x + 9x2 = 0 Solving -116 + -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'. -12.88888889 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '12.88888889' to each side of the equation. -12.88888889 + -1.888888889x + 12.88888889 + x2 = 0 + 12.88888889 Reorder the terms: -12.88888889 + 12.88888889 + -1.888888889x + x2 = 0 + 12.88888889 Combine like terms: -12.88888889 + 12.88888889 = 0.00000000 0.00000000 + -1.888888889x + x2 = 0 + 12.88888889 -1.888888889x + x2 = 0 + 12.88888889 Combine like terms: 0 + 12.88888889 = 12.88888889 -1.888888889x + x2 = 12.88888889 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 = 12.88888889 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = 12.88888889 + 0.8919753087 Combine like terms: 12.88888889 + 0.8919753087 = 13.7808641987 0.8919753087 + -1.888888889x + x2 = 13.7808641987 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 13.7808641987 Calculate the square root of the right side: 3.712258638 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 3.712258638 and -3.712258638.Subproblem 1
x + -0.9444444445 = 3.712258638 Simplifying x + -0.9444444445 = 3.712258638 Reorder the terms: -0.9444444445 + x = 3.712258638 Solving -0.9444444445 + x = 3.712258638 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 = 3.712258638 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 3.712258638 + 0.9444444445 x = 3.712258638 + 0.9444444445 Combine like terms: 3.712258638 + 0.9444444445 = 4.6567030825 x = 4.6567030825 Simplifying x = 4.6567030825Subproblem 2
x + -0.9444444445 = -3.712258638 Simplifying x + -0.9444444445 = -3.712258638 Reorder the terms: -0.9444444445 + x = -3.712258638 Solving -0.9444444445 + x = -3.712258638 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 = -3.712258638 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -3.712258638 + 0.9444444445 x = -3.712258638 + 0.9444444445 Combine like terms: -3.712258638 + 0.9444444445 = -2.7678141935 x = -2.7678141935 Simplifying x = -2.7678141935Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.6567030825, -2.7678141935}
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