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Simplifying 8x2 + -34x + -8 = 0 Reorder the terms: -8 + -34x + 8x2 = 0 Solving -8 + -34x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -17x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -17x + 4x2)' equal to zero and attempt to solve: Simplifying -4 + -17x + 4x2 = 0 Solving -4 + -17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -4.25x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -4.25x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -4.25x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4.25x + x2 = 0 + 1 -4.25x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4.25x + x2 = 1 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = 1 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = 1 + 4.515625 Combine like terms: 1 + 4.515625 = 5.515625 4.515625 + -4.25x + x2 = 5.515625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 5.515625 Calculate the square root of the right side: 2.348536779 Break this problem into two subproblems by setting (x + -2.125) equal to 2.348536779 and -2.348536779.Subproblem 1
x + -2.125 = 2.348536779 Simplifying x + -2.125 = 2.348536779 Reorder the terms: -2.125 + x = 2.348536779 Solving -2.125 + x = 2.348536779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 2.348536779 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 2.348536779 + 2.125 x = 2.348536779 + 2.125 Combine like terms: 2.348536779 + 2.125 = 4.473536779 x = 4.473536779 Simplifying x = 4.473536779Subproblem 2
x + -2.125 = -2.348536779 Simplifying x + -2.125 = -2.348536779 Reorder the terms: -2.125 + x = -2.348536779 Solving -2.125 + x = -2.348536779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -2.348536779 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -2.348536779 + 2.125 x = -2.348536779 + 2.125 Combine like terms: -2.348536779 + 2.125 = -0.223536779 x = -0.223536779 Simplifying x = -0.223536779Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.473536779, -0.223536779}Solution
x = {4.473536779, -0.223536779}
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