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Simplifying 4x2 + 144x + 4 = 0 Reorder the terms: 4 + 144x + 4x2 = 0 Solving 4 + 144x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 36x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 36x + x2)' equal to zero and attempt to solve: Simplifying 1 + 36x + x2 = 0 Solving 1 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 36x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 36x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 36x + x2 = 0 + -1 36x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 36x + x2 = -1 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = -1 + 324 Reorder the terms: 324 + 36x + x2 = -1 + 324 Combine like terms: -1 + 324 = 323 324 + 36x + x2 = 323 Factor a perfect square on the left side: (x + 18)(x + 18) = 323 Calculate the square root of the right side: 17.972200756 Break this problem into two subproblems by setting (x + 18) equal to 17.972200756 and -17.972200756.Subproblem 1
x + 18 = 17.972200756 Simplifying x + 18 = 17.972200756 Reorder the terms: 18 + x = 17.972200756 Solving 18 + x = 17.972200756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 17.972200756 + -18 Combine like terms: 18 + -18 = 0 0 + x = 17.972200756 + -18 x = 17.972200756 + -18 Combine like terms: 17.972200756 + -18 = -0.027799244 x = -0.027799244 Simplifying x = -0.027799244Subproblem 2
x + 18 = -17.972200756 Simplifying x + 18 = -17.972200756 Reorder the terms: 18 + x = -17.972200756 Solving 18 + x = -17.972200756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -17.972200756 + -18 Combine like terms: 18 + -18 = 0 0 + x = -17.972200756 + -18 x = -17.972200756 + -18 Combine like terms: -17.972200756 + -18 = -35.972200756 x = -35.972200756 Simplifying x = -35.972200756Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.027799244, -35.972200756}Solution
x = {-0.027799244, -35.972200756}
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