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Simplifying 2x2 + 4x + -110 = 0 Reorder the terms: -110 + 4x + 2x2 = 0 Solving -110 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-55 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-55 + 2x + x2)' equal to zero and attempt to solve: Simplifying -55 + 2x + x2 = 0 Solving -55 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 2x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + 2x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 2x + x2 = 0 + 55 2x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 2x + x2 = 55 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 55 + 1 Reorder the terms: 1 + 2x + x2 = 55 + 1 Combine like terms: 55 + 1 = 56 1 + 2x + x2 = 56 Factor a perfect square on the left side: (x + 1)(x + 1) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + 1) equal to 7.483314774 and -7.483314774.Subproblem 1
x + 1 = 7.483314774 Simplifying x + 1 = 7.483314774 Reorder the terms: 1 + x = 7.483314774 Solving 1 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 7.483314774 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.483314774 + -1 x = 7.483314774 + -1 Combine like terms: 7.483314774 + -1 = 6.483314774 x = 6.483314774 Simplifying x = 6.483314774Subproblem 2
x + 1 = -7.483314774 Simplifying x + 1 = -7.483314774 Reorder the terms: 1 + x = -7.483314774 Solving 1 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -7.483314774 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.483314774 + -1 x = -7.483314774 + -1 Combine like terms: -7.483314774 + -1 = -8.483314774 x = -8.483314774 Simplifying x = -8.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.483314774, -8.483314774}Solution
x = {6.483314774, -8.483314774}
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