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Simplifying 8.16x2 + 3.42x = 5.93 Reorder the terms: 3.42x + 8.16x2 = 5.93 Solving 3.42x + 8.16x2 = 5.93 Solving for variable 'x'. Reorder the terms: -5.93 + 3.42x + 8.16x2 = 5.93 + -5.93 Combine like terms: 5.93 + -5.93 = 0.00 -5.93 + 3.42x + 8.16x2 = 0.00 Begin completing the square. Divide all terms by 8.16 the coefficient of the squared term: Divide each side by '8.16'. -0.7267156863 + 0.4191176471x + x2 = 0 Move the constant term to the right: Add '0.7267156863' to each side of the equation. -0.7267156863 + 0.4191176471x + 0.7267156863 + x2 = 0 + 0.7267156863 Reorder the terms: -0.7267156863 + 0.7267156863 + 0.4191176471x + x2 = 0 + 0.7267156863 Combine like terms: -0.7267156863 + 0.7267156863 = 0.0000000000 0.0000000000 + 0.4191176471x + x2 = 0 + 0.7267156863 0.4191176471x + x2 = 0 + 0.7267156863 Combine like terms: 0 + 0.7267156863 = 0.7267156863 0.4191176471x + x2 = 0.7267156863 The x term is 0.4191176471x. Take half its coefficient (0.2095588236). Square it (0.04391490055) and add it to both sides. Add '0.04391490055' to each side of the equation. 0.4191176471x + 0.04391490055 + x2 = 0.7267156863 + 0.04391490055 Reorder the terms: 0.04391490055 + 0.4191176471x + x2 = 0.7267156863 + 0.04391490055 Combine like terms: 0.7267156863 + 0.04391490055 = 0.77063058685 0.04391490055 + 0.4191176471x + x2 = 0.77063058685 Factor a perfect square on the left side: (x + 0.2095588236)(x + 0.2095588236) = 0.77063058685 Calculate the square root of the right side: 0.877855675 Break this problem into two subproblems by setting (x + 0.2095588236) equal to 0.877855675 and -0.877855675.Subproblem 1
x + 0.2095588236 = 0.877855675 Simplifying x + 0.2095588236 = 0.877855675 Reorder the terms: 0.2095588236 + x = 0.877855675 Solving 0.2095588236 + x = 0.877855675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2095588236' to each side of the equation. 0.2095588236 + -0.2095588236 + x = 0.877855675 + -0.2095588236 Combine like terms: 0.2095588236 + -0.2095588236 = 0.0000000000 0.0000000000 + x = 0.877855675 + -0.2095588236 x = 0.877855675 + -0.2095588236 Combine like terms: 0.877855675 + -0.2095588236 = 0.6682968514 x = 0.6682968514 Simplifying x = 0.6682968514Subproblem 2
x + 0.2095588236 = -0.877855675 Simplifying x + 0.2095588236 = -0.877855675 Reorder the terms: 0.2095588236 + x = -0.877855675 Solving 0.2095588236 + x = -0.877855675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2095588236' to each side of the equation. 0.2095588236 + -0.2095588236 + x = -0.877855675 + -0.2095588236 Combine like terms: 0.2095588236 + -0.2095588236 = 0.0000000000 0.0000000000 + x = -0.877855675 + -0.2095588236 x = -0.877855675 + -0.2095588236 Combine like terms: -0.877855675 + -0.2095588236 = -1.0874144986 x = -1.0874144986 Simplifying x = -1.0874144986Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6682968514, -1.0874144986}
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