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Simplifying 3X2 + -24X = -4 Reorder the terms: -24X + 3X2 = -4 Solving -24X + 3X2 = -4 Solving for variable 'X'. Reorder the terms: 4 + -24X + 3X2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + -24X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + -8X + X2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -8X + -1.333333333 + X2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -8X + X2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -8X + X2 = 0 + -1.333333333 -8X + X2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -8X + X2 = -1.333333333 The X term is -8X. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8X + 16 + X2 = -1.333333333 + 16 Reorder the terms: 16 + -8X + X2 = -1.333333333 + 16 Combine like terms: -1.333333333 + 16 = 14.666666667 16 + -8X + X2 = 14.666666667 Factor a perfect square on the left side: (X + -4)(X + -4) = 14.666666667 Calculate the square root of the right side: 3.829708431 Break this problem into two subproblems by setting (X + -4) equal to 3.829708431 and -3.829708431.Subproblem 1
X + -4 = 3.829708431 Simplifying X + -4 = 3.829708431 Reorder the terms: -4 + X = 3.829708431 Solving -4 + X = 3.829708431 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = 3.829708431 + 4 Combine like terms: -4 + 4 = 0 0 + X = 3.829708431 + 4 X = 3.829708431 + 4 Combine like terms: 3.829708431 + 4 = 7.829708431 X = 7.829708431 Simplifying X = 7.829708431Subproblem 2
X + -4 = -3.829708431 Simplifying X + -4 = -3.829708431 Reorder the terms: -4 + X = -3.829708431 Solving -4 + X = -3.829708431 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = -3.829708431 + 4 Combine like terms: -4 + 4 = 0 0 + X = -3.829708431 + 4 X = -3.829708431 + 4 Combine like terms: -3.829708431 + 4 = 0.170291569 X = 0.170291569 Simplifying X = 0.170291569Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.829708431, 0.170291569}
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