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Simplifying 2x2 + -2x + -110 = 0 Reorder the terms: -110 + -2x + 2x2 = 0 Solving -110 + -2x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-55 + -1x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-55 + -1x + x2)' equal to zero and attempt to solve: Simplifying -55 + -1x + x2 = 0 Solving -55 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + -1x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + -1x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -1x + x2 = 0 + 55 -1x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 -1x + x2 = 55 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 55 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 55 + 0.25 Combine like terms: 55 + 0.25 = 55.25 0.25 + -1x + x2 = 55.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + -0.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + -0.5 = 7.433034374 Simplifying x + -0.5 = 7.433034374 Reorder the terms: -0.5 + x = 7.433034374 Solving -0.5 + x = 7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 7.433034374 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 7.433034374 + 0.5 x = 7.433034374 + 0.5 Combine like terms: 7.433034374 + 0.5 = 7.933034374 x = 7.933034374 Simplifying x = 7.933034374Subproblem 2
x + -0.5 = -7.433034374 Simplifying x + -0.5 = -7.433034374 Reorder the terms: -0.5 + x = -7.433034374 Solving -0.5 + x = -7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -7.433034374 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -7.433034374 + 0.5 x = -7.433034374 + 0.5 Combine like terms: -7.433034374 + 0.5 = -6.933034374 x = -6.933034374 Simplifying x = -6.933034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.933034374, -6.933034374}Solution
x = {7.933034374, -6.933034374}
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