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Simplifying 16x2 + -72x + 9 = 0 Reorder the terms: 9 + -72x + 16x2 = 0 Solving 9 + -72x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.5625 + -4.5x + x2 = 0 Move the constant term to the right: Add '-0.5625' to each side of the equation. 0.5625 + -4.5x + -0.5625 + x2 = 0 + -0.5625 Reorder the terms: 0.5625 + -0.5625 + -4.5x + x2 = 0 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + -4.5x + x2 = 0 + -0.5625 -4.5x + x2 = 0 + -0.5625 Combine like terms: 0 + -0.5625 = -0.5625 -4.5x + x2 = -0.5625 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 = -0.5625 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -0.5625 + 5.0625 Combine like terms: -0.5625 + 5.0625 = 4.5 5.0625 + -4.5x + x2 = 4.5 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x + -2.25) equal to 2.121320344 and -2.121320344.Subproblem 1
x + -2.25 = 2.121320344 Simplifying x + -2.25 = 2.121320344 Reorder the terms: -2.25 + x = 2.121320344 Solving -2.25 + x = 2.121320344 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 = 2.121320344 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.121320344 + 2.25 x = 2.121320344 + 2.25 Combine like terms: 2.121320344 + 2.25 = 4.371320344 x = 4.371320344 Simplifying x = 4.371320344Subproblem 2
x + -2.25 = -2.121320344 Simplifying x + -2.25 = -2.121320344 Reorder the terms: -2.25 + x = -2.121320344 Solving -2.25 + x = -2.121320344 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 = -2.121320344 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.121320344 + 2.25 x = -2.121320344 + 2.25 Combine like terms: -2.121320344 + 2.25 = 0.128679656 x = 0.128679656 Simplifying x = 0.128679656Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.371320344, 0.128679656}
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