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Simplifying 2x2 + 16x + -20 = 0 Reorder the terms: -20 + 16x + 2x2 = 0 Solving -20 + 16x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 8x + x2)' equal to zero and attempt to solve: Simplifying -10 + 8x + x2 = 0 Solving -10 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 8x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 8x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 8x + x2 = 0 + 10 8x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 8x + x2 = 10 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 = 10 + 16 Reorder the terms: 16 + 8x + x2 = 10 + 16 Combine like terms: 10 + 16 = 26 16 + 8x + x2 = 26 Factor a perfect square on the left side: (x + 4)(x + 4) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + 4) equal to 5.099019514 and -5.099019514.Subproblem 1
x + 4 = 5.099019514 Simplifying x + 4 = 5.099019514 Reorder the terms: 4 + x = 5.099019514 Solving 4 + x = 5.099019514 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 = 5.099019514 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.099019514 + -4 x = 5.099019514 + -4 Combine like terms: 5.099019514 + -4 = 1.099019514 x = 1.099019514 Simplifying x = 1.099019514Subproblem 2
x + 4 = -5.099019514 Simplifying x + 4 = -5.099019514 Reorder the terms: 4 + x = -5.099019514 Solving 4 + x = -5.099019514 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 = -5.099019514 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.099019514 + -4 x = -5.099019514 + -4 Combine like terms: -5.099019514 + -4 = -9.099019514 x = -9.099019514 Simplifying x = -9.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.099019514, -9.099019514}Solution
x = {1.099019514, -9.099019514}
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