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Simplifying 12x(x + -4) = 12x + -24 Reorder the terms: 12x(-4 + x) = 12x + -24 (-4 * 12x + x * 12x) = 12x + -24 (-48x + 12x2) = 12x + -24 Reorder the terms: -48x + 12x2 = -24 + 12x Solving -48x + 12x2 = -24 + 12x Solving for variable 'x'. Reorder the terms: 24 + -48x + -12x + 12x2 = -24 + 12x + 24 + -12x Combine like terms: -48x + -12x = -60x 24 + -60x + 12x2 = -24 + 12x + 24 + -12x Reorder the terms: 24 + -60x + 12x2 = -24 + 24 + 12x + -12x Combine like terms: -24 + 24 = 0 24 + -60x + 12x2 = 0 + 12x + -12x 24 + -60x + 12x2 = 12x + -12x Combine like terms: 12x + -12x = 0 24 + -60x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(2 + -5x + x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(2 + -5x + x2)' equal to zero and attempt to solve: Simplifying 2 + -5x + x2 = 0 Solving 2 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x + x2 = 0 + -2 -5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -5x + x2 = -2 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -2 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -2 + 6.25 Combine like terms: -2 + 6.25 = 4.25 6.25 + -5x + x2 = 4.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -2.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -2.5 = 2.061552813 Simplifying x + -2.5 = 2.061552813 Reorder the terms: -2.5 + x = 2.061552813 Solving -2.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.061552813 + 2.5 x = 2.061552813 + 2.5 Combine like terms: 2.061552813 + 2.5 = 4.561552813 x = 4.561552813 Simplifying x = 4.561552813Subproblem 2
x + -2.5 = -2.061552813 Simplifying x + -2.5 = -2.061552813 Reorder the terms: -2.5 + x = -2.061552813 Solving -2.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.061552813 + 2.5 x = -2.061552813 + 2.5 Combine like terms: -2.061552813 + 2.5 = 0.438447187 x = 0.438447187 Simplifying x = 0.438447187Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.561552813, 0.438447187}Solution
x = {4.561552813, 0.438447187}
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