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Simplifying 8x2 + 48x = 24 Reorder the terms: 48x + 8x2 = 24 Solving 48x + 8x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 48x + 8x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 48x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-3 + 6x + x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-3 + 6x + x2)' equal to zero and attempt to solve: Simplifying -3 + 6x + x2 = 0 Solving -3 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 6x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 6x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6x + x2 = 0 + 3 6x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 6x + x2 = 3 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 = 3 + 9 Reorder the terms: 9 + 6x + x2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + 6x + x2 = 12 Factor a perfect square on the left side: (x + 3)(x + 3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 3) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 3 = 3.464101615 Simplifying x + 3 = 3.464101615 Reorder the terms: 3 + x = 3.464101615 Solving 3 + x = 3.464101615 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 = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.464101615 + -3 x = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 x = 0.464101615 Simplifying x = 0.464101615Subproblem 2
x + 3 = -3.464101615 Simplifying x + 3 = -3.464101615 Reorder the terms: 3 + x = -3.464101615 Solving 3 + x = -3.464101615 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 = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.464101615 + -3 x = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 x = -6.464101615 Simplifying x = -6.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.464101615, -6.464101615}Solution
x = {0.464101615, -6.464101615}
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