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Simplifying 81x2 + -36x + -36x + 16 = 48 Reorder the terms: 16 + -36x + -36x + 81x2 = 48 Combine like terms: -36x + -36x = -72x 16 + -72x + 81x2 = 48 Solving 16 + -72x + 81x2 = 48 Solving for variable 'x'. Reorder the terms: 16 + -48 + -72x + 81x2 = 48 + -48 Combine like terms: 16 + -48 = -32 -32 + -72x + 81x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -32 + -72x + 81x2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.3950617284 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.3950617284' to each side of the equation. -0.3950617284 + -0.8888888889x + 0.3950617284 + x2 = 0 + 0.3950617284 Reorder the terms: -0.3950617284 + 0.3950617284 + -0.8888888889x + x2 = 0 + 0.3950617284 Combine like terms: -0.3950617284 + 0.3950617284 = 0.0000000000 0.0000000000 + -0.8888888889x + x2 = 0 + 0.3950617284 -0.8888888889x + x2 = 0 + 0.3950617284 Combine like terms: 0 + 0.3950617284 = 0.3950617284 -0.8888888889x + x2 = 0.3950617284 The x term is -0.8888888889x. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889x + 0.1975308642 + x2 = 0.3950617284 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 0.3950617284 + 0.1975308642 Combine like terms: 0.3950617284 + 0.1975308642 = 0.5925925926 0.1975308642 + -0.8888888889x + x2 = 0.5925925926 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 0.5925925926 Calculate the square root of the right side: 0.769800359 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 0.769800359 and -0.769800359.Subproblem 1
x + -0.4444444445 = 0.769800359 Simplifying x + -0.4444444445 = 0.769800359 Reorder the terms: -0.4444444445 + x = 0.769800359 Solving -0.4444444445 + x = 0.769800359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 0.769800359 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 0.769800359 + 0.4444444445 x = 0.769800359 + 0.4444444445 Combine like terms: 0.769800359 + 0.4444444445 = 1.2142448035 x = 1.2142448035 Simplifying x = 1.2142448035Subproblem 2
x + -0.4444444445 = -0.769800359 Simplifying x + -0.4444444445 = -0.769800359 Reorder the terms: -0.4444444445 + x = -0.769800359 Solving -0.4444444445 + x = -0.769800359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -0.769800359 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -0.769800359 + 0.4444444445 x = -0.769800359 + 0.4444444445 Combine like terms: -0.769800359 + 0.4444444445 = -0.3253559145 x = -0.3253559145 Simplifying x = -0.3253559145Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2142448035, -0.3253559145}
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