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Simplifying 8x2 + 21x + 4 = 0 Reorder the terms: 4 + 21x + 8x2 = 0 Solving 4 + 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'. 0.5 + 2.625x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 2.625x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 2.625x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 2.625x + x2 = 0 + -0.5 2.625x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 2.625x + x2 = -0.5 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 = -0.5 + 1.72265625 Reorder the terms: 1.72265625 + 2.625x + x2 = -0.5 + 1.72265625 Combine like terms: -0.5 + 1.72265625 = 1.22265625 1.72265625 + 2.625x + x2 = 1.22265625 Factor a perfect square on the left side: (x + 1.3125)(x + 1.3125) = 1.22265625 Calculate the square root of the right side: 1.105737876 Break this problem into two subproblems by setting (x + 1.3125) equal to 1.105737876 and -1.105737876.Subproblem 1
x + 1.3125 = 1.105737876 Simplifying x + 1.3125 = 1.105737876 Reorder the terms: 1.3125 + x = 1.105737876 Solving 1.3125 + x = 1.105737876 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 = 1.105737876 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = 1.105737876 + -1.3125 x = 1.105737876 + -1.3125 Combine like terms: 1.105737876 + -1.3125 = -0.206762124 x = -0.206762124 Simplifying x = -0.206762124Subproblem 2
x + 1.3125 = -1.105737876 Simplifying x + 1.3125 = -1.105737876 Reorder the terms: 1.3125 + x = -1.105737876 Solving 1.3125 + x = -1.105737876 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 = -1.105737876 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = -1.105737876 + -1.3125 x = -1.105737876 + -1.3125 Combine like terms: -1.105737876 + -1.3125 = -2.418237876 x = -2.418237876 Simplifying x = -2.418237876Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.206762124, -2.418237876}
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