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Simplifying 4x2 + -64x + -80 = 0 Reorder the terms: -80 + -64x + 4x2 = 0 Solving -80 + -64x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-20 + -16x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-20 + -16x + x2)' equal to zero and attempt to solve: Simplifying -20 + -16x + x2 = 0 Solving -20 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -16x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -16x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -16x + x2 = 0 + 20 -16x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -16x + x2 = 20 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 20 + 64 Reorder the terms: 64 + -16x + x2 = 20 + 64 Combine like terms: 20 + 64 = 84 64 + -16x + x2 = 84 Factor a perfect square on the left side: (x + -8)(x + -8) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + -8) equal to 9.16515139 and -9.16515139.Subproblem 1
x + -8 = 9.16515139 Simplifying x + -8 = 9.16515139 Reorder the terms: -8 + x = 9.16515139 Solving -8 + x = 9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 9.16515139 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.16515139 + 8 x = 9.16515139 + 8 Combine like terms: 9.16515139 + 8 = 17.16515139 x = 17.16515139 Simplifying x = 17.16515139Subproblem 2
x + -8 = -9.16515139 Simplifying x + -8 = -9.16515139 Reorder the terms: -8 + x = -9.16515139 Solving -8 + x = -9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -9.16515139 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.16515139 + 8 x = -9.16515139 + 8 Combine like terms: -9.16515139 + 8 = -1.16515139 x = -1.16515139 Simplifying x = -1.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.16515139, -1.16515139}Solution
x = {17.16515139, -1.16515139}
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