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Simplifying 4x2 + -6x2 + -72x + 4 = 0 Reorder the terms: 4 + -72x + 4x2 + -6x2 = 0 Combine like terms: 4x2 + -6x2 = -2x2 4 + -72x + -2x2 = 0 Solving 4 + -72x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -36x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -36x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -36x + -1x2 = 0 Solving 2 + -36x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 36x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 36x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 36x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 36x + x2 = 0 + 2 36x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 36x + x2 = 2 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 = 2 + 324 Reorder the terms: 324 + 36x + x2 = 2 + 324 Combine like terms: 2 + 324 = 326 324 + 36x + x2 = 326 Factor a perfect square on the left side: (x + 18)(x + 18) = 326 Calculate the square root of the right side: 18.055470085 Break this problem into two subproblems by setting (x + 18) equal to 18.055470085 and -18.055470085.Subproblem 1
x + 18 = 18.055470085 Simplifying x + 18 = 18.055470085 Reorder the terms: 18 + x = 18.055470085 Solving 18 + x = 18.055470085 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 = 18.055470085 + -18 Combine like terms: 18 + -18 = 0 0 + x = 18.055470085 + -18 x = 18.055470085 + -18 Combine like terms: 18.055470085 + -18 = 0.055470085 x = 0.055470085 Simplifying x = 0.055470085Subproblem 2
x + 18 = -18.055470085 Simplifying x + 18 = -18.055470085 Reorder the terms: 18 + x = -18.055470085 Solving 18 + x = -18.055470085 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 = -18.055470085 + -18 Combine like terms: 18 + -18 = 0 0 + x = -18.055470085 + -18 x = -18.055470085 + -18 Combine like terms: -18.055470085 + -18 = -36.055470085 x = -36.055470085 Simplifying x = -36.055470085Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.055470085, -36.055470085}Solution
x = {0.055470085, -36.055470085}
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