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Simplifying 81x2 + 64x = -6 Reorder the terms: 64x + 81x2 = -6 Solving 64x + 81x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + 64x + 81x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 64x + 81x2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. 0.07407407407 + 0.7901234568x + x2 = 0 Move the constant term to the right: Add '-0.07407407407' to each side of the equation. 0.07407407407 + 0.7901234568x + -0.07407407407 + x2 = 0 + -0.07407407407 Reorder the terms: 0.07407407407 + -0.07407407407 + 0.7901234568x + x2 = 0 + -0.07407407407 Combine like terms: 0.07407407407 + -0.07407407407 = 0.00000000000 0.00000000000 + 0.7901234568x + x2 = 0 + -0.07407407407 0.7901234568x + x2 = 0 + -0.07407407407 Combine like terms: 0 + -0.07407407407 = -0.07407407407 0.7901234568x + x2 = -0.07407407407 The x term is 0.7901234568x. Take half its coefficient (0.3950617284). Square it (0.1560737692) and add it to both sides. Add '0.1560737692' to each side of the equation. 0.7901234568x + 0.1560737692 + x2 = -0.07407407407 + 0.1560737692 Reorder the terms: 0.1560737692 + 0.7901234568x + x2 = -0.07407407407 + 0.1560737692 Combine like terms: -0.07407407407 + 0.1560737692 = 0.08199969513 0.1560737692 + 0.7901234568x + x2 = 0.08199969513 Factor a perfect square on the left side: (x + 0.3950617284)(x + 0.3950617284) = 0.08199969513 Calculate the square root of the right side: 0.286355889 Break this problem into two subproblems by setting (x + 0.3950617284) equal to 0.286355889 and -0.286355889.Subproblem 1
x + 0.3950617284 = 0.286355889 Simplifying x + 0.3950617284 = 0.286355889 Reorder the terms: 0.3950617284 + x = 0.286355889 Solving 0.3950617284 + x = 0.286355889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3950617284' to each side of the equation. 0.3950617284 + -0.3950617284 + x = 0.286355889 + -0.3950617284 Combine like terms: 0.3950617284 + -0.3950617284 = 0.0000000000 0.0000000000 + x = 0.286355889 + -0.3950617284 x = 0.286355889 + -0.3950617284 Combine like terms: 0.286355889 + -0.3950617284 = -0.1087058394 x = -0.1087058394 Simplifying x = -0.1087058394Subproblem 2
x + 0.3950617284 = -0.286355889 Simplifying x + 0.3950617284 = -0.286355889 Reorder the terms: 0.3950617284 + x = -0.286355889 Solving 0.3950617284 + x = -0.286355889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3950617284' to each side of the equation. 0.3950617284 + -0.3950617284 + x = -0.286355889 + -0.3950617284 Combine like terms: 0.3950617284 + -0.3950617284 = 0.0000000000 0.0000000000 + x = -0.286355889 + -0.3950617284 x = -0.286355889 + -0.3950617284 Combine like terms: -0.286355889 + -0.3950617284 = -0.6814176174 x = -0.6814176174 Simplifying x = -0.6814176174Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1087058394, -0.6814176174}
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