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Simplifying 9x2 + -5x + -540 = 0 Reorder the terms: -540 + -5x + 9x2 = 0 Solving -540 + -5x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -60 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -0.5555555556x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -0.5555555556x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -0.5555555556x + x2 = 0 + 60 -0.5555555556x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -0.5555555556x + x2 = 60 The x term is -0.5555555556x. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556x + 0.07716049384 + x2 = 60 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 60 + 0.07716049384 Combine like terms: 60 + 0.07716049384 = 60.07716049384 0.07716049384 + -0.5555555556x + x2 = 60.07716049384 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 60.07716049384 Calculate the square root of the right side: 7.750945781 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 7.750945781 and -7.750945781.Subproblem 1
x + -0.2777777778 = 7.750945781 Simplifying x + -0.2777777778 = 7.750945781 Reorder the terms: -0.2777777778 + x = 7.750945781 Solving -0.2777777778 + x = 7.750945781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = 7.750945781 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 7.750945781 + 0.2777777778 x = 7.750945781 + 0.2777777778 Combine like terms: 7.750945781 + 0.2777777778 = 8.0287235588 x = 8.0287235588 Simplifying x = 8.0287235588Subproblem 2
x + -0.2777777778 = -7.750945781 Simplifying x + -0.2777777778 = -7.750945781 Reorder the terms: -0.2777777778 + x = -7.750945781 Solving -0.2777777778 + x = -7.750945781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = -7.750945781 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -7.750945781 + 0.2777777778 x = -7.750945781 + 0.2777777778 Combine like terms: -7.750945781 + 0.2777777778 = -7.4731680032 x = -7.4731680032 Simplifying x = -7.4731680032Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.0287235588, -7.4731680032}
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