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Simplifying 10x2 + -82x + 81 = 0 Reorder the terms: 81 + -82x + 10x2 = 0 Solving 81 + -82x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 8.1 + -8.2x + x2 = 0 Move the constant term to the right: Add '-8.1' to each side of the equation. 8.1 + -8.2x + -8.1 + x2 = 0 + -8.1 Reorder the terms: 8.1 + -8.1 + -8.2x + x2 = 0 + -8.1 Combine like terms: 8.1 + -8.1 = 0.0 0.0 + -8.2x + x2 = 0 + -8.1 -8.2x + x2 = 0 + -8.1 Combine like terms: 0 + -8.1 = -8.1 -8.2x + x2 = -8.1 The x term is -8.2x. Take half its coefficient (-4.1). Square it (16.81) and add it to both sides. Add '16.81' to each side of the equation. -8.2x + 16.81 + x2 = -8.1 + 16.81 Reorder the terms: 16.81 + -8.2x + x2 = -8.1 + 16.81 Combine like terms: -8.1 + 16.81 = 8.71 16.81 + -8.2x + x2 = 8.71 Factor a perfect square on the left side: (x + -4.1)(x + -4.1) = 8.71 Calculate the square root of the right side: 2.951270913 Break this problem into two subproblems by setting (x + -4.1) equal to 2.951270913 and -2.951270913.Subproblem 1
x + -4.1 = 2.951270913 Simplifying x + -4.1 = 2.951270913 Reorder the terms: -4.1 + x = 2.951270913 Solving -4.1 + x = 2.951270913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.1' to each side of the equation. -4.1 + 4.1 + x = 2.951270913 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + x = 2.951270913 + 4.1 x = 2.951270913 + 4.1 Combine like terms: 2.951270913 + 4.1 = 7.051270913 x = 7.051270913 Simplifying x = 7.051270913Subproblem 2
x + -4.1 = -2.951270913 Simplifying x + -4.1 = -2.951270913 Reorder the terms: -4.1 + x = -2.951270913 Solving -4.1 + x = -2.951270913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.1' to each side of the equation. -4.1 + 4.1 + x = -2.951270913 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + x = -2.951270913 + 4.1 x = -2.951270913 + 4.1 Combine like terms: -2.951270913 + 4.1 = 1.148729087 x = 1.148729087 Simplifying x = 1.148729087Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.051270913, 1.148729087}
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