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Simplifying 0 = 3x2 + -18x + 5 Reorder the terms: 0 = 5 + -18x + 3x2 Solving 0 = 5 + -18x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + 18x + -3x2 = 5 + -18x + 3x2 + -5 + 18x + -3x2 Reorder the terms: -5 + 18x + -3x2 = 5 + -5 + -18x + 18x + 3x2 + -3x2 Combine like terms: 5 + -5 = 0 -5 + 18x + -3x2 = 0 + -18x + 18x + 3x2 + -3x2 -5 + 18x + -3x2 = -18x + 18x + 3x2 + -3x2 Combine like terms: -18x + 18x = 0 -5 + 18x + -3x2 = 0 + 3x2 + -3x2 -5 + 18x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -5 + 18x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.666666667 + -6x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -6x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -6x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -6x + x2 = 0 + -1.666666667 -6x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -6x + x2 = -1.666666667 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -1.666666667 + 9 Reorder the terms: 9 + -6x + x2 = -1.666666667 + 9 Combine like terms: -1.666666667 + 9 = 7.333333333 9 + -6x + x2 = 7.333333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 7.333333333 Calculate the square root of the right side: 2.708012801 Break this problem into two subproblems by setting (x + -3) equal to 2.708012801 and -2.708012801.Subproblem 1
x + -3 = 2.708012801 Simplifying x + -3 = 2.708012801 Reorder the terms: -3 + x = 2.708012801 Solving -3 + x = 2.708012801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.708012801 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.708012801 + 3 x = 2.708012801 + 3 Combine like terms: 2.708012801 + 3 = 5.708012801 x = 5.708012801 Simplifying x = 5.708012801Subproblem 2
x + -3 = -2.708012801 Simplifying x + -3 = -2.708012801 Reorder the terms: -3 + x = -2.708012801 Solving -3 + x = -2.708012801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.708012801 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.708012801 + 3 x = -2.708012801 + 3 Combine like terms: -2.708012801 + 3 = 0.291987199 x = 0.291987199 Simplifying x = 0.291987199Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.708012801, 0.291987199}
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