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Simplifying 4(x2 + 20x + -12) = 0 Reorder the terms: 4(-12 + 20x + x2) = 0 (-12 * 4 + 20x * 4 + x2 * 4) = 0 (-48 + 80x + 4x2) = 0 Solving -48 + 80x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + 20x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-12 + 20x + x2)' equal to zero and attempt to solve: Simplifying -12 + 20x + x2 = 0 Solving -12 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 20x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 20x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 20x + x2 = 0 + 12 20x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 20x + x2 = 12 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 12 + 100 Reorder the terms: 100 + 20x + x2 = 12 + 100 Combine like terms: 12 + 100 = 112 100 + 20x + x2 = 112 Factor a perfect square on the left side: (x + 10)(x + 10) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (x + 10) equal to 10.583005244 and -10.583005244.Subproblem 1
x + 10 = 10.583005244 Simplifying x + 10 = 10.583005244 Reorder the terms: 10 + x = 10.583005244 Solving 10 + x = 10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 10.583005244 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.583005244 + -10 x = 10.583005244 + -10 Combine like terms: 10.583005244 + -10 = 0.583005244 x = 0.583005244 Simplifying x = 0.583005244Subproblem 2
x + 10 = -10.583005244 Simplifying x + 10 = -10.583005244 Reorder the terms: 10 + x = -10.583005244 Solving 10 + x = -10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -10.583005244 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.583005244 + -10 x = -10.583005244 + -10 Combine like terms: -10.583005244 + -10 = -20.583005244 x = -20.583005244 Simplifying x = -20.583005244Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.583005244, -20.583005244}Solution
x = {0.583005244, -20.583005244}
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