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Simplifying 2x2 + 16x + -80 = 0 Reorder the terms: -80 + 16x + 2x2 = 0 Solving -80 + 16x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + 8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + 8x + x2)' equal to zero and attempt to solve: Simplifying -40 + 8x + x2 = 0 Solving -40 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 8x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 8x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 8x + x2 = 0 + 40 8x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 8x + x2 = 40 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 40 + 16 Reorder the terms: 16 + 8x + x2 = 40 + 16 Combine like terms: 40 + 16 = 56 16 + 8x + x2 = 56 Factor a perfect square on the left side: (x + 4)(x + 4) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + 4) equal to 7.483314774 and -7.483314774.Subproblem 1
x + 4 = 7.483314774 Simplifying x + 4 = 7.483314774 Reorder the terms: 4 + x = 7.483314774 Solving 4 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 7.483314774 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.483314774 + -4 x = 7.483314774 + -4 Combine like terms: 7.483314774 + -4 = 3.483314774 x = 3.483314774 Simplifying x = 3.483314774Subproblem 2
x + 4 = -7.483314774 Simplifying x + 4 = -7.483314774 Reorder the terms: 4 + x = -7.483314774 Solving 4 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -7.483314774 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.483314774 + -4 x = -7.483314774 + -4 Combine like terms: -7.483314774 + -4 = -11.483314774 x = -11.483314774 Simplifying x = -11.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.483314774, -11.483314774}Solution
x = {3.483314774, -11.483314774}
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