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Simplifying 3x2 + 19x = 360 Reorder the terms: 19x + 3x2 = 360 Solving 19x + 3x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 19x + 3x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 19x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -120 + 6.333333333x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 6.333333333x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 6.333333333x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 6.333333333x + x2 = 0 + 120 6.333333333x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 6.333333333x + x2 = 120 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 = 120 + 10.02777778 Reorder the terms: 10.02777778 + 6.333333333x + x2 = 120 + 10.02777778 Combine like terms: 120 + 10.02777778 = 130.02777778 10.02777778 + 6.333333333x + x2 = 130.02777778 Factor a perfect square on the left side: (x + 3.166666667)(x + 3.166666667) = 130.02777778 Calculate the square root of the right side: 11.402972322 Break this problem into two subproblems by setting (x + 3.166666667) equal to 11.402972322 and -11.402972322.Subproblem 1
x + 3.166666667 = 11.402972322 Simplifying x + 3.166666667 = 11.402972322 Reorder the terms: 3.166666667 + x = 11.402972322 Solving 3.166666667 + x = 11.402972322 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 = 11.402972322 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + x = 11.402972322 + -3.166666667 x = 11.402972322 + -3.166666667 Combine like terms: 11.402972322 + -3.166666667 = 8.236305655 x = 8.236305655 Simplifying x = 8.236305655Subproblem 2
x + 3.166666667 = -11.402972322 Simplifying x + 3.166666667 = -11.402972322 Reorder the terms: 3.166666667 + x = -11.402972322 Solving 3.166666667 + x = -11.402972322 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 = -11.402972322 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + x = -11.402972322 + -3.166666667 x = -11.402972322 + -3.166666667 Combine like terms: -11.402972322 + -3.166666667 = -14.569638989 x = -14.569638989 Simplifying x = -14.569638989Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.236305655, -14.569638989}
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