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Simplifying 17x + -9x2 = 5 Solving 17x + -9x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 17x + -9x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 17x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 0.5555555556 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + -1.888888889x + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + -1.888888889x + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + -1.888888889x + x2 = 0 + -0.5555555556 -1.888888889x + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 -1.888888889x + x2 = -0.5555555556 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 = -0.5555555556 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = -0.5555555556 + 0.8919753087 Combine like terms: -0.5555555556 + 0.8919753087 = 0.3364197531 0.8919753087 + -1.888888889x + x2 = 0.3364197531 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 0.3364197531 Calculate the square root of the right side: 0.580017028 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 0.580017028 and -0.580017028.Subproblem 1
x + -0.9444444445 = 0.580017028 Simplifying x + -0.9444444445 = 0.580017028 Reorder the terms: -0.9444444445 + x = 0.580017028 Solving -0.9444444445 + x = 0.580017028 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 = 0.580017028 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 0.580017028 + 0.9444444445 x = 0.580017028 + 0.9444444445 Combine like terms: 0.580017028 + 0.9444444445 = 1.5244614725 x = 1.5244614725 Simplifying x = 1.5244614725Subproblem 2
x + -0.9444444445 = -0.580017028 Simplifying x + -0.9444444445 = -0.580017028 Reorder the terms: -0.9444444445 + x = -0.580017028 Solving -0.9444444445 + x = -0.580017028 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 = -0.580017028 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -0.580017028 + 0.9444444445 x = -0.580017028 + 0.9444444445 Combine like terms: -0.580017028 + 0.9444444445 = 0.3644274165 x = 0.3644274165 Simplifying x = 0.3644274165Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5244614725, 0.3644274165}
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