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Simplifying 8x2 + 185x + 21 = 0 Reorder the terms: 21 + 185x + 8x2 = 0 Solving 21 + 185x + 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 + 23.125x + x2 = 0 Move the constant term to the right: Add '-2.625' to each side of the equation. 2.625 + 23.125x + -2.625 + x2 = 0 + -2.625 Reorder the terms: 2.625 + -2.625 + 23.125x + x2 = 0 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + 23.125x + x2 = 0 + -2.625 23.125x + x2 = 0 + -2.625 Combine like terms: 0 + -2.625 = -2.625 23.125x + x2 = -2.625 The x term is 23.125x. Take half its coefficient (11.5625). Square it (133.6914063) and add it to both sides. Add '133.6914063' to each side of the equation. 23.125x + 133.6914063 + x2 = -2.625 + 133.6914063 Reorder the terms: 133.6914063 + 23.125x + x2 = -2.625 + 133.6914063 Combine like terms: -2.625 + 133.6914063 = 131.0664063 133.6914063 + 23.125x + x2 = 131.0664063 Factor a perfect square on the left side: (x + 11.5625)(x + 11.5625) = 131.0664063 Calculate the square root of the right side: 11.448423747 Break this problem into two subproblems by setting (x + 11.5625) equal to 11.448423747 and -11.448423747.Subproblem 1
x + 11.5625 = 11.448423747 Simplifying x + 11.5625 = 11.448423747 Reorder the terms: 11.5625 + x = 11.448423747 Solving 11.5625 + x = 11.448423747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5625' to each side of the equation. 11.5625 + -11.5625 + x = 11.448423747 + -11.5625 Combine like terms: 11.5625 + -11.5625 = 0.0000 0.0000 + x = 11.448423747 + -11.5625 x = 11.448423747 + -11.5625 Combine like terms: 11.448423747 + -11.5625 = -0.114076253 x = -0.114076253 Simplifying x = -0.114076253Subproblem 2
x + 11.5625 = -11.448423747 Simplifying x + 11.5625 = -11.448423747 Reorder the terms: 11.5625 + x = -11.448423747 Solving 11.5625 + x = -11.448423747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5625' to each side of the equation. 11.5625 + -11.5625 + x = -11.448423747 + -11.5625 Combine like terms: 11.5625 + -11.5625 = 0.0000 0.0000 + x = -11.448423747 + -11.5625 x = -11.448423747 + -11.5625 Combine like terms: -11.448423747 + -11.5625 = -23.010923747 x = -23.010923747 Simplifying x = -23.010923747Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.114076253, -23.010923747}
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