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Simplifying 8x2 + 6 + 53x = 0 Reorder the terms: 6 + 53x + 8x2 = 0 Solving 6 + 53x + 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'. 0.75 + 6.625x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 6.625x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 6.625x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 6.625x + x2 = 0 + -0.75 6.625x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 6.625x + x2 = -0.75 The x term is 6.625x. Take half its coefficient (3.3125). Square it (10.97265625) and add it to both sides. Add '10.97265625' to each side of the equation. 6.625x + 10.97265625 + x2 = -0.75 + 10.97265625 Reorder the terms: 10.97265625 + 6.625x + x2 = -0.75 + 10.97265625 Combine like terms: -0.75 + 10.97265625 = 10.22265625 10.97265625 + 6.625x + x2 = 10.22265625 Factor a perfect square on the left side: (x + 3.3125)(x + 3.3125) = 10.22265625 Calculate the square root of the right side: 3.197288891 Break this problem into two subproblems by setting (x + 3.3125) equal to 3.197288891 and -3.197288891.Subproblem 1
x + 3.3125 = 3.197288891 Simplifying x + 3.3125 = 3.197288891 Reorder the terms: 3.3125 + x = 3.197288891 Solving 3.3125 + x = 3.197288891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.3125' to each side of the equation. 3.3125 + -3.3125 + x = 3.197288891 + -3.3125 Combine like terms: 3.3125 + -3.3125 = 0.0000 0.0000 + x = 3.197288891 + -3.3125 x = 3.197288891 + -3.3125 Combine like terms: 3.197288891 + -3.3125 = -0.115211109 x = -0.115211109 Simplifying x = -0.115211109Subproblem 2
x + 3.3125 = -3.197288891 Simplifying x + 3.3125 = -3.197288891 Reorder the terms: 3.3125 + x = -3.197288891 Solving 3.3125 + x = -3.197288891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.3125' to each side of the equation. 3.3125 + -3.3125 + x = -3.197288891 + -3.3125 Combine like terms: 3.3125 + -3.3125 = 0.0000 0.0000 + x = -3.197288891 + -3.3125 x = -3.197288891 + -3.3125 Combine like terms: -3.197288891 + -3.3125 = -6.509788891 x = -6.509788891 Simplifying x = -6.509788891Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.115211109, -6.509788891}
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