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Simplifying 2x2 + -11x2 + 17x + -6 = 0 Reorder the terms: -6 + 17x + 2x2 + -11x2 = 0 Combine like terms: 2x2 + -11x2 = -9x2 -6 + 17x + -9x2 = 0 Solving -6 + 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'. 0.6666666667 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -1.888888889x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -1.888888889x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -1.888888889x + x2 = 0 + -0.6666666667 -1.888888889x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -1.888888889x + x2 = -0.6666666667 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 = -0.6666666667 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = -0.6666666667 + 0.8919753087 Combine like terms: -0.6666666667 + 0.8919753087 = 0.225308642 0.8919753087 + -1.888888889x + x2 = 0.225308642 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 0.225308642 Calculate the square root of the right side: 0.474666875 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 0.474666875 and -0.474666875.Subproblem 1
x + -0.9444444445 = 0.474666875 Simplifying x + -0.9444444445 = 0.474666875 Reorder the terms: -0.9444444445 + x = 0.474666875 Solving -0.9444444445 + x = 0.474666875 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 = 0.474666875 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 0.474666875 + 0.9444444445 x = 0.474666875 + 0.9444444445 Combine like terms: 0.474666875 + 0.9444444445 = 1.4191113195 x = 1.4191113195 Simplifying x = 1.4191113195Subproblem 2
x + -0.9444444445 = -0.474666875 Simplifying x + -0.9444444445 = -0.474666875 Reorder the terms: -0.9444444445 + x = -0.474666875 Solving -0.9444444445 + x = -0.474666875 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 = -0.474666875 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -0.474666875 + 0.9444444445 x = -0.474666875 + 0.9444444445 Combine like terms: -0.474666875 + 0.9444444445 = 0.4697775695 x = 0.4697775695 Simplifying x = 0.4697775695Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4191113195, 0.4697775695}
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