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Simplifying 8x2 + 21x + -400 = 0 Reorder the terms: -400 + 21x + 8x2 = 0 Solving -400 + 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'. -50 + 2.625x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 2.625x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 2.625x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 2.625x + x2 = 0 + 50 2.625x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 2.625x + x2 = 50 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 = 50 + 1.72265625 Reorder the terms: 1.72265625 + 2.625x + x2 = 50 + 1.72265625 Combine like terms: 50 + 1.72265625 = 51.72265625 1.72265625 + 2.625x + x2 = 51.72265625 Factor a perfect square on the left side: (x + 1.3125)(x + 1.3125) = 51.72265625 Calculate the square root of the right side: 7.191846512 Break this problem into two subproblems by setting (x + 1.3125) equal to 7.191846512 and -7.191846512.Subproblem 1
x + 1.3125 = 7.191846512 Simplifying x + 1.3125 = 7.191846512 Reorder the terms: 1.3125 + x = 7.191846512 Solving 1.3125 + x = 7.191846512 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 = 7.191846512 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = 7.191846512 + -1.3125 x = 7.191846512 + -1.3125 Combine like terms: 7.191846512 + -1.3125 = 5.879346512 x = 5.879346512 Simplifying x = 5.879346512Subproblem 2
x + 1.3125 = -7.191846512 Simplifying x + 1.3125 = -7.191846512 Reorder the terms: 1.3125 + x = -7.191846512 Solving 1.3125 + x = -7.191846512 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 = -7.191846512 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = -7.191846512 + -1.3125 x = -7.191846512 + -1.3125 Combine like terms: -7.191846512 + -1.3125 = -8.504346512 x = -8.504346512 Simplifying x = -8.504346512Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.879346512, -8.504346512}
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