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Simplifying 16x2 = 72x + 81 Reorder the terms: 16x2 = 81 + 72x Solving 16x2 = 81 + 72x Solving for variable 'x'. Reorder the terms: -81 + -72x + 16x2 = 81 + 72x + -81 + -72x Reorder the terms: -81 + -72x + 16x2 = 81 + -81 + 72x + -72x Combine like terms: 81 + -81 = 0 -81 + -72x + 16x2 = 0 + 72x + -72x -81 + -72x + 16x2 = 72x + -72x Combine like terms: 72x + -72x = 0 -81 + -72x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.0625 + -4.5x + x2 = 0 Move the constant term to the right: Add '5.0625' to each side of the equation. -5.0625 + -4.5x + 5.0625 + x2 = 0 + 5.0625 Reorder the terms: -5.0625 + 5.0625 + -4.5x + x2 = 0 + 5.0625 Combine like terms: -5.0625 + 5.0625 = 0.0000 0.0000 + -4.5x + x2 = 0 + 5.0625 -4.5x + x2 = 0 + 5.0625 Combine like terms: 0 + 5.0625 = 5.0625 -4.5x + x2 = 5.0625 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 = 5.0625 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 5.0625 + 5.0625 Combine like terms: 5.0625 + 5.0625 = 10.125 5.0625 + -4.5x + x2 = 10.125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 10.125 Calculate the square root of the right side: 3.181980515 Break this problem into two subproblems by setting (x + -2.25) equal to 3.181980515 and -3.181980515.Subproblem 1
x + -2.25 = 3.181980515 Simplifying x + -2.25 = 3.181980515 Reorder the terms: -2.25 + x = 3.181980515 Solving -2.25 + x = 3.181980515 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 = 3.181980515 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 3.181980515 + 2.25 x = 3.181980515 + 2.25 Combine like terms: 3.181980515 + 2.25 = 5.431980515 x = 5.431980515 Simplifying x = 5.431980515Subproblem 2
x + -2.25 = -3.181980515 Simplifying x + -2.25 = -3.181980515 Reorder the terms: -2.25 + x = -3.181980515 Solving -2.25 + x = -3.181980515 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 = -3.181980515 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -3.181980515 + 2.25 x = -3.181980515 + 2.25 Combine like terms: -3.181980515 + 2.25 = -0.931980515 x = -0.931980515 Simplifying x = -0.931980515Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.431980515, -0.931980515}
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