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Simplifying 3(4x2 + 24x + -1) = 0 Reorder the terms: 3(-1 + 24x + 4x2) = 0 (-1 * 3 + 24x * 3 + 4x2 * 3) = 0 (-3 + 72x + 12x2) = 0 Solving -3 + 72x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 24x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 24x + 4x2)' equal to zero and attempt to solve: Simplifying -1 + 24x + 4x2 = 0 Solving -1 + 24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 6x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 6x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 6x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 6x + x2 = 0 + 0.25 6x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 6x + x2 = 0.25 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 = 0.25 + 9 Reorder the terms: 9 + 6x + x2 = 0.25 + 9 Combine like terms: 0.25 + 9 = 9.25 9 + 6x + x2 = 9.25 Factor a perfect square on the left side: (x + 3)(x + 3) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + 3) equal to 3.041381265 and -3.041381265.Subproblem 1
x + 3 = 3.041381265 Simplifying x + 3 = 3.041381265 Reorder the terms: 3 + x = 3.041381265 Solving 3 + x = 3.041381265 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 = 3.041381265 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.041381265 + -3 x = 3.041381265 + -3 Combine like terms: 3.041381265 + -3 = 0.041381265 x = 0.041381265 Simplifying x = 0.041381265Subproblem 2
x + 3 = -3.041381265 Simplifying x + 3 = -3.041381265 Reorder the terms: 3 + x = -3.041381265 Solving 3 + x = -3.041381265 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 = -3.041381265 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.041381265 + -3 x = -3.041381265 + -3 Combine like terms: -3.041381265 + -3 = -6.041381265 x = -6.041381265 Simplifying x = -6.041381265Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.041381265, -6.041381265}Solution
x = {0.041381265, -6.041381265}
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