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Simplifying 3x2 + 19x = 54 Reorder the terms: 19x + 3x2 = 54 Solving 19x + 3x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + 19x + 3x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 19x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -18 + 6.333333333x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 6.333333333x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 6.333333333x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 6.333333333x + x2 = 0 + 18 6.333333333x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 6.333333333x + x2 = 18 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 = 18 + 10.02777778 Reorder the terms: 10.02777778 + 6.333333333x + x2 = 18 + 10.02777778 Combine like terms: 18 + 10.02777778 = 28.02777778 10.02777778 + 6.333333333x + x2 = 28.02777778 Factor a perfect square on the left side: (x + 3.166666667)(x + 3.166666667) = 28.02777778 Calculate the square root of the right side: 5.294126725 Break this problem into two subproblems by setting (x + 3.166666667) equal to 5.294126725 and -5.294126725.Subproblem 1
x + 3.166666667 = 5.294126725 Simplifying x + 3.166666667 = 5.294126725 Reorder the terms: 3.166666667 + x = 5.294126725 Solving 3.166666667 + x = 5.294126725 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 = 5.294126725 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + x = 5.294126725 + -3.166666667 x = 5.294126725 + -3.166666667 Combine like terms: 5.294126725 + -3.166666667 = 2.127460058 x = 2.127460058 Simplifying x = 2.127460058Subproblem 2
x + 3.166666667 = -5.294126725 Simplifying x + 3.166666667 = -5.294126725 Reorder the terms: 3.166666667 + x = -5.294126725 Solving 3.166666667 + x = -5.294126725 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 = -5.294126725 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + x = -5.294126725 + -3.166666667 x = -5.294126725 + -3.166666667 Combine like terms: -5.294126725 + -3.166666667 = -8.460793392 x = -8.460793392 Simplifying x = -8.460793392Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.127460058, -8.460793392}
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