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Simplifying 6x2 + 23x = 36 Reorder the terms: 23x + 6x2 = 36 Solving 23x + 6x2 = 36 Solving for variable 'x'. Reorder the terms: -36 + 23x + 6x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 23x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6 + 3.833333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 3.833333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 3.833333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3.833333333x + x2 = 0 + 6 3.833333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 3.833333333x + x2 = 6 The x term is 3.833333333x. Take half its coefficient (1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. 3.833333333x + 3.673611112 + x2 = 6 + 3.673611112 Reorder the terms: 3.673611112 + 3.833333333x + x2 = 6 + 3.673611112 Combine like terms: 6 + 3.673611112 = 9.673611112 3.673611112 + 3.833333333x + x2 = 9.673611112 Factor a perfect square on the left side: (x + 1.916666667)(x + 1.916666667) = 9.673611112 Calculate the square root of the right side: 3.110242935 Break this problem into two subproblems by setting (x + 1.916666667) equal to 3.110242935 and -3.110242935.Subproblem 1
x + 1.916666667 = 3.110242935 Simplifying x + 1.916666667 = 3.110242935 Reorder the terms: 1.916666667 + x = 3.110242935 Solving 1.916666667 + x = 3.110242935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + x = 3.110242935 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = 3.110242935 + -1.916666667 x = 3.110242935 + -1.916666667 Combine like terms: 3.110242935 + -1.916666667 = 1.193576268 x = 1.193576268 Simplifying x = 1.193576268Subproblem 2
x + 1.916666667 = -3.110242935 Simplifying x + 1.916666667 = -3.110242935 Reorder the terms: 1.916666667 + x = -3.110242935 Solving 1.916666667 + x = -3.110242935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + x = -3.110242935 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = -3.110242935 + -1.916666667 x = -3.110242935 + -1.916666667 Combine like terms: -3.110242935 + -1.916666667 = -5.026909602 x = -5.026909602 Simplifying x = -5.026909602Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.193576268, -5.026909602}
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