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Simplifying 81x2 + 162x + 73 = 0 Reorder the terms: 73 + 162x + 81x2 = 0 Solving 73 + 162x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. 0.9012345679 + 2x + x2 = 0 Move the constant term to the right: Add '-0.9012345679' to each side of the equation. 0.9012345679 + 2x + -0.9012345679 + x2 = 0 + -0.9012345679 Reorder the terms: 0.9012345679 + -0.9012345679 + 2x + x2 = 0 + -0.9012345679 Combine like terms: 0.9012345679 + -0.9012345679 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + -0.9012345679 2x + x2 = 0 + -0.9012345679 Combine like terms: 0 + -0.9012345679 = -0.9012345679 2x + x2 = -0.9012345679 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.9012345679 + 1 Reorder the terms: 1 + 2x + x2 = -0.9012345679 + 1 Combine like terms: -0.9012345679 + 1 = 0.0987654321 1 + 2x + x2 = 0.0987654321 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.0987654321 Calculate the square root of the right side: 0.314269681 Break this problem into two subproblems by setting (x + 1) equal to 0.314269681 and -0.314269681.Subproblem 1
x + 1 = 0.314269681 Simplifying x + 1 = 0.314269681 Reorder the terms: 1 + x = 0.314269681 Solving 1 + x = 0.314269681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.314269681 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.314269681 + -1 x = 0.314269681 + -1 Combine like terms: 0.314269681 + -1 = -0.685730319 x = -0.685730319 Simplifying x = -0.685730319Subproblem 2
x + 1 = -0.314269681 Simplifying x + 1 = -0.314269681 Reorder the terms: 1 + x = -0.314269681 Solving 1 + x = -0.314269681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.314269681 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.314269681 + -1 x = -0.314269681 + -1 Combine like terms: -0.314269681 + -1 = -1.314269681 x = -1.314269681 Simplifying x = -1.314269681Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.685730319, -1.314269681}
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