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Simplifying 8x2 + 6x + -21 = 0 Reorder the terms: -21 + 6x + 8x2 = 0 Solving -21 + 6x + 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 + 0.75x + x2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + 0.75x + 2.625 + x2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + 0.75x + x2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + 0.75x + x2 = 0 + 2.625 0.75x + x2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 0.75x + x2 = 2.625 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 2.625 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 2.625 + 0.140625 Combine like terms: 2.625 + 0.140625 = 2.765625 0.140625 + 0.75x + x2 = 2.765625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 2.765625 Calculate the square root of the right side: 1.663016837 Break this problem into two subproblems by setting (x + 0.375) equal to 1.663016837 and -1.663016837.Subproblem 1
x + 0.375 = 1.663016837 Simplifying x + 0.375 = 1.663016837 Reorder the terms: 0.375 + x = 1.663016837 Solving 0.375 + x = 1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 1.663016837 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.663016837 + -0.375 x = 1.663016837 + -0.375 Combine like terms: 1.663016837 + -0.375 = 1.288016837 x = 1.288016837 Simplifying x = 1.288016837Subproblem 2
x + 0.375 = -1.663016837 Simplifying x + 0.375 = -1.663016837 Reorder the terms: 0.375 + x = -1.663016837 Solving 0.375 + x = -1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -1.663016837 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.663016837 + -0.375 x = -1.663016837 + -0.375 Combine like terms: -1.663016837 + -0.375 = -2.038016837 x = -2.038016837 Simplifying x = -2.038016837Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.288016837, -2.038016837}
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