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Simplifying 8x2 + 53x + -5 = 0 Reorder the terms: -5 + 53x + 8x2 = 0 Solving -5 + 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'. -0.625 + 6.625x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 6.625x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 6.625x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 6.625x + x2 = 0 + 0.625 6.625x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 6.625x + x2 = 0.625 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 = 0.625 + 10.97265625 Reorder the terms: 10.97265625 + 6.625x + x2 = 0.625 + 10.97265625 Combine like terms: 0.625 + 10.97265625 = 11.59765625 10.97265625 + 6.625x + x2 = 11.59765625 Factor a perfect square on the left side: (x + 3.3125)(x + 3.3125) = 11.59765625 Calculate the square root of the right side: 3.405533181 Break this problem into two subproblems by setting (x + 3.3125) equal to 3.405533181 and -3.405533181.Subproblem 1
x + 3.3125 = 3.405533181 Simplifying x + 3.3125 = 3.405533181 Reorder the terms: 3.3125 + x = 3.405533181 Solving 3.3125 + x = 3.405533181 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 = 3.405533181 + -3.3125 Combine like terms: 3.3125 + -3.3125 = 0.0000 0.0000 + x = 3.405533181 + -3.3125 x = 3.405533181 + -3.3125 Combine like terms: 3.405533181 + -3.3125 = 0.093033181 x = 0.093033181 Simplifying x = 0.093033181Subproblem 2
x + 3.3125 = -3.405533181 Simplifying x + 3.3125 = -3.405533181 Reorder the terms: 3.3125 + x = -3.405533181 Solving 3.3125 + x = -3.405533181 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 = -3.405533181 + -3.3125 Combine like terms: 3.3125 + -3.3125 = 0.0000 0.0000 + x = -3.405533181 + -3.3125 x = -3.405533181 + -3.3125 Combine like terms: -3.405533181 + -3.3125 = -6.718033181 x = -6.718033181 Simplifying x = -6.718033181Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.093033181, -6.718033181}
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