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Simplifying 3x2 + -24x = 3 Reorder the terms: -24x + 3x2 = 3 Solving -24x + 3x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -24x + 3x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -24x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -8x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -8x + x2)' equal to zero and attempt to solve: Simplifying -1 + -8x + x2 = 0 Solving -1 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -8x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -8x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8x + x2 = 0 + 1 -8x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -8x + x2 = 1 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 = 1 + 16 Reorder the terms: 16 + -8x + x2 = 1 + 16 Combine like terms: 1 + 16 = 17 16 + -8x + x2 = 17 Factor a perfect square on the left side: (x + -4)(x + -4) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + -4) equal to 4.123105626 and -4.123105626.Subproblem 1
x + -4 = 4.123105626 Simplifying x + -4 = 4.123105626 Reorder the terms: -4 + x = 4.123105626 Solving -4 + x = 4.123105626 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 = 4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.123105626 + 4 x = 4.123105626 + 4 Combine like terms: 4.123105626 + 4 = 8.123105626 x = 8.123105626 Simplifying x = 8.123105626Subproblem 2
x + -4 = -4.123105626 Simplifying x + -4 = -4.123105626 Reorder the terms: -4 + x = -4.123105626 Solving -4 + x = -4.123105626 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 = -4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.123105626 + 4 x = -4.123105626 + 4 Combine like terms: -4.123105626 + 4 = -0.123105626 x = -0.123105626 Simplifying x = -0.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.123105626, -0.123105626}Solution
x = {8.123105626, -0.123105626}
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