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Simplifying -3X2 + 24X = 27 Reorder the terms: 24X + -3X2 = 27 Solving 24X + -3X2 = 27 Solving for variable 'X'. Reorder the terms: -27 + 24X + -3X2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 24X + -3X2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 8X + -1X2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + 8X + -1X2)' equal to zero and attempt to solve: Simplifying -9 + 8X + -1X2 = 0 Solving -9 + 8X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 9 + -8X + X2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -8X + -9 + X2 = 0 + -9 Reorder the terms: 9 + -9 + -8X + X2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8X + X2 = 0 + -9 -8X + X2 = 0 + -9 Combine like terms: 0 + -9 = -9 -8X + X2 = -9 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 = -9 + 16 Reorder the terms: 16 + -8X + X2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + -8X + X2 = 7 Factor a perfect square on the left side: (X + -4)(X + -4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (X + -4) equal to 2.645751311 and -2.645751311.Subproblem 1
X + -4 = 2.645751311 Simplifying X + -4 = 2.645751311 Reorder the terms: -4 + X = 2.645751311 Solving -4 + X = 2.645751311 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 = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + X = 2.645751311 + 4 X = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 X = 6.645751311 Simplifying X = 6.645751311Subproblem 2
X + -4 = -2.645751311 Simplifying X + -4 = -2.645751311 Reorder the terms: -4 + X = -2.645751311 Solving -4 + X = -2.645751311 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 = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + X = -2.645751311 + 4 X = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 X = 1.354248689 Simplifying X = 1.354248689Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.645751311, 1.354248689}Solution
X = {6.645751311, 1.354248689}
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