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Simplifying 3x2 + -19x = 24 Reorder the terms: -19x + 3x2 = 24 Solving -19x + 3x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + -19x + 3x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -19x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + -6.333333333x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -6.333333333x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -6.333333333x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6.333333333x + x2 = 0 + 8 -6.333333333x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6.333333333x + x2 = 8 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 = 8 + 10.02777778 Reorder the terms: 10.02777778 + -6.333333333x + x2 = 8 + 10.02777778 Combine like terms: 8 + 10.02777778 = 18.02777778 10.02777778 + -6.333333333x + x2 = 18.02777778 Factor a perfect square on the left side: (x + -3.166666667)(x + -3.166666667) = 18.02777778 Calculate the square root of the right side: 4.245913068 Break this problem into two subproblems by setting (x + -3.166666667) equal to 4.245913068 and -4.245913068.Subproblem 1
x + -3.166666667 = 4.245913068 Simplifying x + -3.166666667 = 4.245913068 Reorder the terms: -3.166666667 + x = 4.245913068 Solving -3.166666667 + x = 4.245913068 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 = 4.245913068 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = 4.245913068 + 3.166666667 x = 4.245913068 + 3.166666667 Combine like terms: 4.245913068 + 3.166666667 = 7.412579735 x = 7.412579735 Simplifying x = 7.412579735Subproblem 2
x + -3.166666667 = -4.245913068 Simplifying x + -3.166666667 = -4.245913068 Reorder the terms: -3.166666667 + x = -4.245913068 Solving -3.166666667 + x = -4.245913068 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 = -4.245913068 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = -4.245913068 + 3.166666667 x = -4.245913068 + 3.166666667 Combine like terms: -4.245913068 + 3.166666667 = -1.079246401 x = -1.079246401 Simplifying x = -1.079246401Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.412579735, -1.079246401}
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