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Simplifying 3x2 + -17x + 18 = 0 Reorder the terms: 18 + -17x + 3x2 = 0 Solving 18 + -17x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 6 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -5.666666667x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -5.666666667x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5.666666667x + x2 = 0 + -6 -5.666666667x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -5.666666667x + x2 = -6 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = -6 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = -6 + 8.027777782 Combine like terms: -6 + 8.027777782 = 2.027777782 8.027777782 + -5.666666667x + x2 = 2.027777782 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 2.027777782 Calculate the square root of the right side: 1.424000626 Break this problem into two subproblems by setting (x + -2.833333334) equal to 1.424000626 and -1.424000626.Subproblem 1
x + -2.833333334 = 1.424000626 Simplifying x + -2.833333334 = 1.424000626 Reorder the terms: -2.833333334 + x = 1.424000626 Solving -2.833333334 + x = 1.424000626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 1.424000626 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 1.424000626 + 2.833333334 x = 1.424000626 + 2.833333334 Combine like terms: 1.424000626 + 2.833333334 = 4.25733396 x = 4.25733396 Simplifying x = 4.25733396Subproblem 2
x + -2.833333334 = -1.424000626 Simplifying x + -2.833333334 = -1.424000626 Reorder the terms: -2.833333334 + x = -1.424000626 Solving -2.833333334 + x = -1.424000626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -1.424000626 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -1.424000626 + 2.833333334 x = -1.424000626 + 2.833333334 Combine like terms: -1.424000626 + 2.833333334 = 1.409332708 x = 1.409332708 Simplifying x = 1.409332708Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.25733396, 1.409332708}
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