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Simplifying 8x2 + -21x + 7 = 0 Reorder the terms: 7 + -21x + 8x2 = 0 Solving 7 + -21x + 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'. 0.875 + -2.625x + x2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -2.625x + -0.875 + x2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -2.625x + x2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -2.625x + x2 = 0 + -0.875 -2.625x + x2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -2.625x + x2 = -0.875 The x term is -2.625x. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625x + 1.72265625 + x2 = -0.875 + 1.72265625 Reorder the terms: 1.72265625 + -2.625x + x2 = -0.875 + 1.72265625 Combine like terms: -0.875 + 1.72265625 = 0.84765625 1.72265625 + -2.625x + x2 = 0.84765625 Factor a perfect square on the left side: (x + -1.3125)(x + -1.3125) = 0.84765625 Calculate the square root of the right side: 0.920682491 Break this problem into two subproblems by setting (x + -1.3125) equal to 0.920682491 and -0.920682491.Subproblem 1
x + -1.3125 = 0.920682491 Simplifying x + -1.3125 = 0.920682491 Reorder the terms: -1.3125 + x = 0.920682491 Solving -1.3125 + x = 0.920682491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = 0.920682491 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = 0.920682491 + 1.3125 x = 0.920682491 + 1.3125 Combine like terms: 0.920682491 + 1.3125 = 2.233182491 x = 2.233182491 Simplifying x = 2.233182491Subproblem 2
x + -1.3125 = -0.920682491 Simplifying x + -1.3125 = -0.920682491 Reorder the terms: -1.3125 + x = -0.920682491 Solving -1.3125 + x = -0.920682491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = -0.920682491 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = -0.920682491 + 1.3125 x = -0.920682491 + 1.3125 Combine like terms: -0.920682491 + 1.3125 = 0.391817509 x = 0.391817509 Simplifying x = 0.391817509Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.233182491, 0.391817509}
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