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Simplifying 6x2 + -23x + -24 = 0 Reorder the terms: -24 + -23x + 6x2 = 0 Solving -24 + -23x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4 + -3.833333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -3.833333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -3.833333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3.833333333x + x2 = 0 + 4 -3.833333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -3.833333333x + x2 = 4 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 = 4 + 3.673611112 Reorder the terms: 3.673611112 + -3.833333333x + x2 = 4 + 3.673611112 Combine like terms: 4 + 3.673611112 = 7.673611112 3.673611112 + -3.833333333x + x2 = 7.673611112 Factor a perfect square on the left side: (x + -1.916666667)(x + -1.916666667) = 7.673611112 Calculate the square root of the right side: 2.770128357 Break this problem into two subproblems by setting (x + -1.916666667) equal to 2.770128357 and -2.770128357.Subproblem 1
x + -1.916666667 = 2.770128357 Simplifying x + -1.916666667 = 2.770128357 Reorder the terms: -1.916666667 + x = 2.770128357 Solving -1.916666667 + x = 2.770128357 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 = 2.770128357 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = 2.770128357 + 1.916666667 x = 2.770128357 + 1.916666667 Combine like terms: 2.770128357 + 1.916666667 = 4.686795024 x = 4.686795024 Simplifying x = 4.686795024Subproblem 2
x + -1.916666667 = -2.770128357 Simplifying x + -1.916666667 = -2.770128357 Reorder the terms: -1.916666667 + x = -2.770128357 Solving -1.916666667 + x = -2.770128357 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 = -2.770128357 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = -2.770128357 + 1.916666667 x = -2.770128357 + 1.916666667 Combine like terms: -2.770128357 + 1.916666667 = -0.85346169 x = -0.85346169 Simplifying x = -0.85346169Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.686795024, -0.85346169}
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