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Simplifying 4x(x + -12) = 20 Reorder the terms: 4x(-12 + x) = 20 (-12 * 4x + x * 4x) = 20 (-48x + 4x2) = 20 Solving -48x + 4x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + -48x + 4x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -48x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -12x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -12x + x2)' equal to zero and attempt to solve: Simplifying -5 + -12x + x2 = 0 Solving -5 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -12x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -12x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -12x + x2 = 0 + 5 -12x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -12x + x2 = 5 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 5 + 36 Reorder the terms: 36 + -12x + x2 = 5 + 36 Combine like terms: 5 + 36 = 41 36 + -12x + x2 = 41 Factor a perfect square on the left side: (x + -6)(x + -6) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + -6) equal to 6.403124237 and -6.403124237.Subproblem 1
x + -6 = 6.403124237 Simplifying x + -6 = 6.403124237 Reorder the terms: -6 + x = 6.403124237 Solving -6 + x = 6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 6.403124237 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.403124237 + 6 x = 6.403124237 + 6 Combine like terms: 6.403124237 + 6 = 12.403124237 x = 12.403124237 Simplifying x = 12.403124237Subproblem 2
x + -6 = -6.403124237 Simplifying x + -6 = -6.403124237 Reorder the terms: -6 + x = -6.403124237 Solving -6 + x = -6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -6.403124237 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.403124237 + 6 x = -6.403124237 + 6 Combine like terms: -6.403124237 + 6 = -0.403124237 x = -0.403124237 Simplifying x = -0.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.403124237, -0.403124237}Solution
x = {12.403124237, -0.403124237}
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