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Simplifying 3x2 + -19x + 18 = 0 Reorder the terms: 18 + -19x + 3x2 = 0 Solving 18 + -19x + 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 + -6.333333333x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -6.333333333x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -6.333333333x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -6.333333333x + x2 = 0 + -6 -6.333333333x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -6.333333333x + x2 = -6 The x term is -6.333333333x. Take half its coefficient (-3.166666667). Square it (10.02777778) and add it to both sides. Add '10.02777778' to each side of the equation. -6.333333333x + 10.02777778 + x2 = -6 + 10.02777778 Reorder the terms: 10.02777778 + -6.333333333x + x2 = -6 + 10.02777778 Combine like terms: -6 + 10.02777778 = 4.02777778 10.02777778 + -6.333333333x + x2 = 4.02777778 Factor a perfect square on the left side: (x + -3.166666667)(x + -3.166666667) = 4.02777778 Calculate the square root of the right side: 2.00693243 Break this problem into two subproblems by setting (x + -3.166666667) equal to 2.00693243 and -2.00693243.Subproblem 1
x + -3.166666667 = 2.00693243 Simplifying x + -3.166666667 = 2.00693243 Reorder the terms: -3.166666667 + x = 2.00693243 Solving -3.166666667 + x = 2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = 2.00693243 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = 2.00693243 + 3.166666667 x = 2.00693243 + 3.166666667 Combine like terms: 2.00693243 + 3.166666667 = 5.173599097 x = 5.173599097 Simplifying x = 5.173599097Subproblem 2
x + -3.166666667 = -2.00693243 Simplifying x + -3.166666667 = -2.00693243 Reorder the terms: -3.166666667 + x = -2.00693243 Solving -3.166666667 + x = -2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = -2.00693243 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = -2.00693243 + 3.166666667 x = -2.00693243 + 3.166666667 Combine like terms: -2.00693243 + 3.166666667 = 1.159734237 x = 1.159734237 Simplifying x = 1.159734237Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.173599097, 1.159734237}
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