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Simplifying 16x2 + -64x + -180 = 0 Reorder the terms: -180 + -64x + 16x2 = 0 Solving -180 + -64x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + -16x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + -16x + 4x2)' equal to zero and attempt to solve: Simplifying -45 + -16x + 4x2 = 0 Solving -45 + -16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + -4x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -4x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -4x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -4x + x2 = 0 + 11.25 -4x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -4x + x2 = 11.25 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 11.25 + 4 Reorder the terms: 4 + -4x + x2 = 11.25 + 4 Combine like terms: 11.25 + 4 = 15.25 4 + -4x + x2 = 15.25 Factor a perfect square on the left side: (x + -2)(x + -2) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + -2) equal to 3.905124838 and -3.905124838.Subproblem 1
x + -2 = 3.905124838 Simplifying x + -2 = 3.905124838 Reorder the terms: -2 + x = 3.905124838 Solving -2 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.905124838 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.905124838 + 2 x = 3.905124838 + 2 Combine like terms: 3.905124838 + 2 = 5.905124838 x = 5.905124838 Simplifying x = 5.905124838Subproblem 2
x + -2 = -3.905124838 Simplifying x + -2 = -3.905124838 Reorder the terms: -2 + x = -3.905124838 Solving -2 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.905124838 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.905124838 + 2 x = -3.905124838 + 2 Combine like terms: -3.905124838 + 2 = -1.905124838 x = -1.905124838 Simplifying x = -1.905124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.905124838, -1.905124838}Solution
x = {5.905124838, -1.905124838}
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