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Simplifying 3X2 = 24X + -18 Reorder the terms: 3X2 = -18 + 24X Solving 3X2 = -18 + 24X Solving for variable 'X'. Reorder the terms: 18 + -24X + 3X2 = -18 + 24X + 18 + -24X Reorder the terms: 18 + -24X + 3X2 = -18 + 18 + 24X + -24X Combine like terms: -18 + 18 = 0 18 + -24X + 3X2 = 0 + 24X + -24X 18 + -24X + 3X2 = 24X + -24X Combine like terms: 24X + -24X = 0 18 + -24X + 3X2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -8X + X2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -8X + X2)' equal to zero and attempt to solve: Simplifying 6 + -8X + X2 = 0 Solving 6 + -8X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -8X + -6 + X2 = 0 + -6 Reorder the terms: 6 + -6 + -8X + X2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -8X + X2 = 0 + -6 -8X + X2 = 0 + -6 Combine like terms: 0 + -6 = -6 -8X + X2 = -6 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 = -6 + 16 Reorder the terms: 16 + -8X + X2 = -6 + 16 Combine like terms: -6 + 16 = 10 16 + -8X + X2 = 10 Factor a perfect square on the left side: (X + -4)(X + -4) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (X + -4) equal to 3.16227766 and -3.16227766.Subproblem 1
X + -4 = 3.16227766 Simplifying X + -4 = 3.16227766 Reorder the terms: -4 + X = 3.16227766 Solving -4 + X = 3.16227766 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 = 3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + X = 3.16227766 + 4 X = 3.16227766 + 4 Combine like terms: 3.16227766 + 4 = 7.16227766 X = 7.16227766 Simplifying X = 7.16227766Subproblem 2
X + -4 = -3.16227766 Simplifying X + -4 = -3.16227766 Reorder the terms: -4 + X = -3.16227766 Solving -4 + X = -3.16227766 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 = -3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + X = -3.16227766 + 4 X = -3.16227766 + 4 Combine like terms: -3.16227766 + 4 = 0.83772234 X = 0.83772234 Simplifying X = 0.83772234Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.16227766, 0.83772234}Solution
X = {7.16227766, 0.83772234}
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