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Simplifying 8x2 + -34x + 21 = -11 Reorder the terms: 21 + -34x + 8x2 = -11 Solving 21 + -34x + 8x2 = -11 Solving for variable 'x'. Reorder the terms: 21 + 11 + -34x + 8x2 = -11 + 11 Combine like terms: 21 + 11 = 32 32 + -34x + 8x2 = -11 + 11 Combine like terms: -11 + 11 = 0 32 + -34x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -17x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + -17x + 4x2)' equal to zero and attempt to solve: Simplifying 16 + -17x + 4x2 = 0 Solving 16 + -17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4 + -4.25x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4.25x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -4.25x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4.25x + x2 = 0 + -4 -4.25x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4.25x + x2 = -4 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 = -4 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = -4 + 4.515625 Combine like terms: -4 + 4.515625 = 0.515625 4.515625 + -4.25x + x2 = 0.515625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (x + -2.125) equal to 0.718070331 and -0.718070331.Subproblem 1
x + -2.125 = 0.718070331 Simplifying x + -2.125 = 0.718070331 Reorder the terms: -2.125 + x = 0.718070331 Solving -2.125 + x = 0.718070331 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 = 0.718070331 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 0.718070331 + 2.125 x = 0.718070331 + 2.125 Combine like terms: 0.718070331 + 2.125 = 2.843070331 x = 2.843070331 Simplifying x = 2.843070331Subproblem 2
x + -2.125 = -0.718070331 Simplifying x + -2.125 = -0.718070331 Reorder the terms: -2.125 + x = -0.718070331 Solving -2.125 + x = -0.718070331 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 = -0.718070331 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -0.718070331 + 2.125 x = -0.718070331 + 2.125 Combine like terms: -0.718070331 + 2.125 = 1.406929669 x = 1.406929669 Simplifying x = 1.406929669Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.843070331, 1.406929669}Solution
x = {2.843070331, 1.406929669}
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