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Simplifying 8x2 + -2x + -22 = 0 Reorder the terms: -22 + -2x + 8x2 = 0 Solving -22 + -2x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + -1x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + -1x + 4x2)' equal to zero and attempt to solve: Simplifying -11 + -1x + 4x2 = 0 Solving -11 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -0.25x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -0.25x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -0.25x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -0.25x + x2 = 0 + 2.75 -0.25x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -0.25x + x2 = 2.75 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 2.75 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 2.75 + 0.015625 Combine like terms: 2.75 + 0.015625 = 2.765625 0.015625 + -0.25x + x2 = 2.765625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 2.765625 Calculate the square root of the right side: 1.663016837 Break this problem into two subproblems by setting (x + -0.125) equal to 1.663016837 and -1.663016837.Subproblem 1
x + -0.125 = 1.663016837 Simplifying x + -0.125 = 1.663016837 Reorder the terms: -0.125 + x = 1.663016837 Solving -0.125 + x = 1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 1.663016837 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.663016837 + 0.125 x = 1.663016837 + 0.125 Combine like terms: 1.663016837 + 0.125 = 1.788016837 x = 1.788016837 Simplifying x = 1.788016837Subproblem 2
x + -0.125 = -1.663016837 Simplifying x + -0.125 = -1.663016837 Reorder the terms: -0.125 + x = -1.663016837 Solving -0.125 + x = -1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -1.663016837 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.663016837 + 0.125 x = -1.663016837 + 0.125 Combine like terms: -1.663016837 + 0.125 = -1.538016837 x = -1.538016837 Simplifying x = -1.538016837Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.788016837, -1.538016837}Solution
x = {1.788016837, -1.538016837}
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