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Simplifying 3x2 + 19x + 3 = 0 Reorder the terms: 3 + 19x + 3x2 = 0 Solving 3 + 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'. 1 + 6.333333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 6.333333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 6.333333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6.333333333x + x2 = 0 + -1 6.333333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 6.333333333x + x2 = -1 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 = -1 + 10.02777778 Reorder the terms: 10.02777778 + 6.333333333x + x2 = -1 + 10.02777778 Combine like terms: -1 + 10.02777778 = 9.02777778 10.02777778 + 6.333333333x + x2 = 9.02777778 Factor a perfect square on the left side: (x + 3.166666667)(x + 3.166666667) = 9.02777778 Calculate the square root of the right side: 3.004626063 Break this problem into two subproblems by setting (x + 3.166666667) equal to 3.004626063 and -3.004626063.Subproblem 1
x + 3.166666667 = 3.004626063 Simplifying x + 3.166666667 = 3.004626063 Reorder the terms: 3.166666667 + x = 3.004626063 Solving 3.166666667 + x = 3.004626063 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 = 3.004626063 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + x = 3.004626063 + -3.166666667 x = 3.004626063 + -3.166666667 Combine like terms: 3.004626063 + -3.166666667 = -0.162040604 x = -0.162040604 Simplifying x = -0.162040604Subproblem 2
x + 3.166666667 = -3.004626063 Simplifying x + 3.166666667 = -3.004626063 Reorder the terms: 3.166666667 + x = -3.004626063 Solving 3.166666667 + x = -3.004626063 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 = -3.004626063 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + x = -3.004626063 + -3.166666667 x = -3.004626063 + -3.166666667 Combine like terms: -3.004626063 + -3.166666667 = -6.17129273 x = -6.17129273 Simplifying x = -6.17129273Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.162040604, -6.17129273}
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