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Simplifying 8x2 + -36x + -405 = 0 Reorder the terms: -405 + -36x + 8x2 = 0 Solving -405 + -36x + 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'. -50.625 + -4.5x + x2 = 0 Move the constant term to the right: Add '50.625' to each side of the equation. -50.625 + -4.5x + 50.625 + x2 = 0 + 50.625 Reorder the terms: -50.625 + 50.625 + -4.5x + x2 = 0 + 50.625 Combine like terms: -50.625 + 50.625 = 0.000 0.000 + -4.5x + x2 = 0 + 50.625 -4.5x + x2 = 0 + 50.625 Combine like terms: 0 + 50.625 = 50.625 -4.5x + x2 = 50.625 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 50.625 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 50.625 + 5.0625 Combine like terms: 50.625 + 5.0625 = 55.6875 5.0625 + -4.5x + x2 = 55.6875 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 55.6875 Calculate the square root of the right side: 7.462405778 Break this problem into two subproblems by setting (x + -2.25) equal to 7.462405778 and -7.462405778.Subproblem 1
x + -2.25 = 7.462405778 Simplifying x + -2.25 = 7.462405778 Reorder the terms: -2.25 + x = 7.462405778 Solving -2.25 + x = 7.462405778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 7.462405778 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 7.462405778 + 2.25 x = 7.462405778 + 2.25 Combine like terms: 7.462405778 + 2.25 = 9.712405778 x = 9.712405778 Simplifying x = 9.712405778Subproblem 2
x + -2.25 = -7.462405778 Simplifying x + -2.25 = -7.462405778 Reorder the terms: -2.25 + x = -7.462405778 Solving -2.25 + x = -7.462405778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -7.462405778 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -7.462405778 + 2.25 x = -7.462405778 + 2.25 Combine like terms: -7.462405778 + 2.25 = -5.212405778 x = -5.212405778 Simplifying x = -5.212405778Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.712405778, -5.212405778}
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