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Simplifying 9x2 + -17x + -2 = 2 Reorder the terms: -2 + -17x + 9x2 = 2 Solving -2 + -17x + 9x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -2 + -17x + 9x2 = 2 + -2 Combine like terms: -2 + -2 = -4 -4 + -17x + 9x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -4 + -17x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -1.888888889x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -1.888888889x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -1.888888889x + x2 = 0 + 0.4444444444 -1.888888889x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -1.888888889x + x2 = 0.4444444444 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 = 0.4444444444 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = 0.4444444444 + 0.8919753087 Combine like terms: 0.4444444444 + 0.8919753087 = 1.3364197531 0.8919753087 + -1.888888889x + x2 = 1.3364197531 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 1.3364197531 Calculate the square root of the right side: 1.156036225 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 1.156036225 and -1.156036225.Subproblem 1
x + -0.9444444445 = 1.156036225 Simplifying x + -0.9444444445 = 1.156036225 Reorder the terms: -0.9444444445 + x = 1.156036225 Solving -0.9444444445 + x = 1.156036225 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 = 1.156036225 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 1.156036225 + 0.9444444445 x = 1.156036225 + 0.9444444445 Combine like terms: 1.156036225 + 0.9444444445 = 2.1004806695 x = 2.1004806695 Simplifying x = 2.1004806695Subproblem 2
x + -0.9444444445 = -1.156036225 Simplifying x + -0.9444444445 = -1.156036225 Reorder the terms: -0.9444444445 + x = -1.156036225 Solving -0.9444444445 + x = -1.156036225 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 = -1.156036225 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -1.156036225 + 0.9444444445 x = -1.156036225 + 0.9444444445 Combine like terms: -1.156036225 + 0.9444444445 = -0.2115917805 x = -0.2115917805 Simplifying x = -0.2115917805Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1004806695, -0.2115917805}
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