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Simplifying 4x2 + -144x + 464 = 0 Reorder the terms: 464 + -144x + 4x2 = 0 Solving 464 + -144x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(116 + -36x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(116 + -36x + x2)' equal to zero and attempt to solve: Simplifying 116 + -36x + x2 = 0 Solving 116 + -36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-116' to each side of the equation. 116 + -36x + -116 + x2 = 0 + -116 Reorder the terms: 116 + -116 + -36x + x2 = 0 + -116 Combine like terms: 116 + -116 = 0 0 + -36x + x2 = 0 + -116 -36x + x2 = 0 + -116 Combine like terms: 0 + -116 = -116 -36x + x2 = -116 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 = -116 + 324 Reorder the terms: 324 + -36x + x2 = -116 + 324 Combine like terms: -116 + 324 = 208 324 + -36x + x2 = 208 Factor a perfect square on the left side: (x + -18)(x + -18) = 208 Calculate the square root of the right side: 14.422205102 Break this problem into two subproblems by setting (x + -18) equal to 14.422205102 and -14.422205102.Subproblem 1
x + -18 = 14.422205102 Simplifying x + -18 = 14.422205102 Reorder the terms: -18 + x = 14.422205102 Solving -18 + x = 14.422205102 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 = 14.422205102 + 18 Combine like terms: -18 + 18 = 0 0 + x = 14.422205102 + 18 x = 14.422205102 + 18 Combine like terms: 14.422205102 + 18 = 32.422205102 x = 32.422205102 Simplifying x = 32.422205102Subproblem 2
x + -18 = -14.422205102 Simplifying x + -18 = -14.422205102 Reorder the terms: -18 + x = -14.422205102 Solving -18 + x = -14.422205102 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 = -14.422205102 + 18 Combine like terms: -18 + 18 = 0 0 + x = -14.422205102 + 18 x = -14.422205102 + 18 Combine like terms: -14.422205102 + 18 = 3.577794898 x = 3.577794898 Simplifying x = 3.577794898Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.422205102, 3.577794898}Solution
x = {32.422205102, 3.577794898}
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