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Simplifying 23X + -5X2 = -24 Solving 23X + -5X2 = -24 Solving for variable 'X'. Reorder the terms: 24 + 23X + -5X2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + 23X + -5X2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -4.8 + -4.6X + X2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -4.6X + 4.8 + X2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -4.6X + X2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -4.6X + X2 = 0 + 4.8 -4.6X + X2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -4.6X + X2 = 4.8 The X term is -4.6X. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6X + 5.29 + X2 = 4.8 + 5.29 Reorder the terms: 5.29 + -4.6X + X2 = 4.8 + 5.29 Combine like terms: 4.8 + 5.29 = 10.09 5.29 + -4.6X + X2 = 10.09 Factor a perfect square on the left side: (X + -2.3)(X + -2.3) = 10.09 Calculate the square root of the right side: 3.176476035 Break this problem into two subproblems by setting (X + -2.3) equal to 3.176476035 and -3.176476035.Subproblem 1
X + -2.3 = 3.176476035 Simplifying X + -2.3 = 3.176476035 Reorder the terms: -2.3 + X = 3.176476035 Solving -2.3 + X = 3.176476035 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + X = 3.176476035 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + X = 3.176476035 + 2.3 X = 3.176476035 + 2.3 Combine like terms: 3.176476035 + 2.3 = 5.476476035 X = 5.476476035 Simplifying X = 5.476476035Subproblem 2
X + -2.3 = -3.176476035 Simplifying X + -2.3 = -3.176476035 Reorder the terms: -2.3 + X = -3.176476035 Solving -2.3 + X = -3.176476035 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + X = -3.176476035 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + X = -3.176476035 + 2.3 X = -3.176476035 + 2.3 Combine like terms: -3.176476035 + 2.3 = -0.876476035 X = -0.876476035 Simplifying X = -0.876476035Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.476476035, -0.876476035}
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