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Simplifying X2 = 6X + 24 Reorder the terms: X2 = 24 + 6X Solving X2 = 24 + 6X Solving for variable 'X'. Reorder the terms: -24 + -6X + X2 = 24 + 6X + -24 + -6X Reorder the terms: -24 + -6X + X2 = 24 + -24 + 6X + -6X Combine like terms: 24 + -24 = 0 -24 + -6X + X2 = 0 + 6X + -6X -24 + -6X + X2 = 6X + -6X Combine like terms: 6X + -6X = 0 -24 + -6X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -6X + 24 + X2 = 0 + 24 Reorder the terms: -24 + 24 + -6X + X2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -6X + X2 = 0 + 24 -6X + X2 = 0 + 24 Combine like terms: 0 + 24 = 24 -6X + X2 = 24 The X term is -6X. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6X + 9 + X2 = 24 + 9 Reorder the terms: 9 + -6X + X2 = 24 + 9 Combine like terms: 24 + 9 = 33 9 + -6X + X2 = 33 Factor a perfect square on the left side: (X + -3)(X + -3) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (X + -3) equal to 5.744562647 and -5.744562647.Subproblem 1
X + -3 = 5.744562647 Simplifying X + -3 = 5.744562647 Reorder the terms: -3 + X = 5.744562647 Solving -3 + X = 5.744562647 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = 5.744562647 + 3 Combine like terms: -3 + 3 = 0 0 + X = 5.744562647 + 3 X = 5.744562647 + 3 Combine like terms: 5.744562647 + 3 = 8.744562647 X = 8.744562647 Simplifying X = 8.744562647Subproblem 2
X + -3 = -5.744562647 Simplifying X + -3 = -5.744562647 Reorder the terms: -3 + X = -5.744562647 Solving -3 + X = -5.744562647 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = -5.744562647 + 3 Combine like terms: -3 + 3 = 0 0 + X = -5.744562647 + 3 X = -5.744562647 + 3 Combine like terms: -5.744562647 + 3 = -2.744562647 X = -2.744562647 Simplifying X = -2.744562647Solution
The solution to the problem is based on the solutions from the subproblems. X = {8.744562647, -2.744562647}
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