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Simplifying 40x2 + 39x + -585 = 0 Reorder the terms: -585 + 39x + 40x2 = 0 Solving -585 + 39x + 40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -14.625 + 0.975x + x2 = 0 Move the constant term to the right: Add '14.625' to each side of the equation. -14.625 + 0.975x + 14.625 + x2 = 0 + 14.625 Reorder the terms: -14.625 + 14.625 + 0.975x + x2 = 0 + 14.625 Combine like terms: -14.625 + 14.625 = 0.000 0.000 + 0.975x + x2 = 0 + 14.625 0.975x + x2 = 0 + 14.625 Combine like terms: 0 + 14.625 = 14.625 0.975x + x2 = 14.625 The x term is 0.975x. Take half its coefficient (0.4875). Square it (0.23765625) and add it to both sides. Add '0.23765625' to each side of the equation. 0.975x + 0.23765625 + x2 = 14.625 + 0.23765625 Reorder the terms: 0.23765625 + 0.975x + x2 = 14.625 + 0.23765625 Combine like terms: 14.625 + 0.23765625 = 14.86265625 0.23765625 + 0.975x + x2 = 14.86265625 Factor a perfect square on the left side: (x + 0.4875)(x + 0.4875) = 14.86265625 Calculate the square root of the right side: 3.85521157 Break this problem into two subproblems by setting (x + 0.4875) equal to 3.85521157 and -3.85521157.Subproblem 1
x + 0.4875 = 3.85521157 Simplifying x + 0.4875 = 3.85521157 Reorder the terms: 0.4875 + x = 3.85521157 Solving 0.4875 + x = 3.85521157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4875' to each side of the equation. 0.4875 + -0.4875 + x = 3.85521157 + -0.4875 Combine like terms: 0.4875 + -0.4875 = 0.0000 0.0000 + x = 3.85521157 + -0.4875 x = 3.85521157 + -0.4875 Combine like terms: 3.85521157 + -0.4875 = 3.36771157 x = 3.36771157 Simplifying x = 3.36771157Subproblem 2
x + 0.4875 = -3.85521157 Simplifying x + 0.4875 = -3.85521157 Reorder the terms: 0.4875 + x = -3.85521157 Solving 0.4875 + x = -3.85521157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4875' to each side of the equation. 0.4875 + -0.4875 + x = -3.85521157 + -0.4875 Combine like terms: 0.4875 + -0.4875 = 0.0000 0.0000 + x = -3.85521157 + -0.4875 x = -3.85521157 + -0.4875 Combine like terms: -3.85521157 + -0.4875 = -4.34271157 x = -4.34271157 Simplifying x = -4.34271157Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.36771157, -4.34271157}
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