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Simplifying 8x2 + -34x + -21 = 0 Reorder the terms: -21 + -34x + 8x2 = 0 Solving -21 + -34x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.625 + -4.25x + x2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + -4.25x + 2.625 + x2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + -4.25x + x2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + -4.25x + x2 = 0 + 2.625 -4.25x + x2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 -4.25x + x2 = 2.625 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 = 2.625 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = 2.625 + 4.515625 Combine like terms: 2.625 + 4.515625 = 7.140625 4.515625 + -4.25x + x2 = 7.140625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 7.140625 Calculate the square root of the right side: 2.672194791 Break this problem into two subproblems by setting (x + -2.125) equal to 2.672194791 and -2.672194791.Subproblem 1
x + -2.125 = 2.672194791 Simplifying x + -2.125 = 2.672194791 Reorder the terms: -2.125 + x = 2.672194791 Solving -2.125 + x = 2.672194791 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 = 2.672194791 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 2.672194791 + 2.125 x = 2.672194791 + 2.125 Combine like terms: 2.672194791 + 2.125 = 4.797194791 x = 4.797194791 Simplifying x = 4.797194791Subproblem 2
x + -2.125 = -2.672194791 Simplifying x + -2.125 = -2.672194791 Reorder the terms: -2.125 + x = -2.672194791 Solving -2.125 + x = -2.672194791 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 = -2.672194791 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -2.672194791 + 2.125 x = -2.672194791 + 2.125 Combine like terms: -2.672194791 + 2.125 = -0.547194791 x = -0.547194791 Simplifying x = -0.547194791Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.797194791, -0.547194791}
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