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Simplifying 24x + 3x2 = 54 Solving 24x + 3x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + 24x + 3x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 24x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-18 + 8x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-18 + 8x + x2)' equal to zero and attempt to solve: Simplifying -18 + 8x + x2 = 0 Solving -18 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 8x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 8x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 8x + x2 = 0 + 18 8x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 8x + x2 = 18 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 = 18 + 16 Reorder the terms: 16 + 8x + x2 = 18 + 16 Combine like terms: 18 + 16 = 34 16 + 8x + x2 = 34 Factor a perfect square on the left side: (x + 4)(x + 4) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + 4) equal to 5.830951895 and -5.830951895.Subproblem 1
x + 4 = 5.830951895 Simplifying x + 4 = 5.830951895 Reorder the terms: 4 + x = 5.830951895 Solving 4 + x = 5.830951895 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 = 5.830951895 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.830951895 + -4 x = 5.830951895 + -4 Combine like terms: 5.830951895 + -4 = 1.830951895 x = 1.830951895 Simplifying x = 1.830951895Subproblem 2
x + 4 = -5.830951895 Simplifying x + 4 = -5.830951895 Reorder the terms: 4 + x = -5.830951895 Solving 4 + x = -5.830951895 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 = -5.830951895 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.830951895 + -4 x = -5.830951895 + -4 Combine like terms: -5.830951895 + -4 = -9.830951895 x = -9.830951895 Simplifying x = -9.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.830951895, -9.830951895}Solution
x = {1.830951895, -9.830951895}
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