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Simplifying 81x2 + -118x + 36 = 0 Reorder the terms: 36 + -118x + 81x2 = 0 Solving 36 + -118x + 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'. 0.4444444444 + -1.456790123x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -1.456790123x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -1.456790123x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -1.456790123x + x2 = 0 + -0.4444444444 -1.456790123x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -1.456790123x + x2 = -0.4444444444 The x term is -1.456790123x. Take half its coefficient (-0.7283950615). Square it (0.5305593656) and add it to both sides. Add '0.5305593656' to each side of the equation. -1.456790123x + 0.5305593656 + x2 = -0.4444444444 + 0.5305593656 Reorder the terms: 0.5305593656 + -1.456790123x + x2 = -0.4444444444 + 0.5305593656 Combine like terms: -0.4444444444 + 0.5305593656 = 0.0861149212 0.5305593656 + -1.456790123x + x2 = 0.0861149212 Factor a perfect square on the left side: (x + -0.7283950615)(x + -0.7283950615) = 0.0861149212 Calculate the square root of the right side: 0.29345344 Break this problem into two subproblems by setting (x + -0.7283950615) equal to 0.29345344 and -0.29345344.Subproblem 1
x + -0.7283950615 = 0.29345344 Simplifying x + -0.7283950615 = 0.29345344 Reorder the terms: -0.7283950615 + x = 0.29345344 Solving -0.7283950615 + x = 0.29345344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7283950615' to each side of the equation. -0.7283950615 + 0.7283950615 + x = 0.29345344 + 0.7283950615 Combine like terms: -0.7283950615 + 0.7283950615 = 0.0000000000 0.0000000000 + x = 0.29345344 + 0.7283950615 x = 0.29345344 + 0.7283950615 Combine like terms: 0.29345344 + 0.7283950615 = 1.0218485015 x = 1.0218485015 Simplifying x = 1.0218485015Subproblem 2
x + -0.7283950615 = -0.29345344 Simplifying x + -0.7283950615 = -0.29345344 Reorder the terms: -0.7283950615 + x = -0.29345344 Solving -0.7283950615 + x = -0.29345344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7283950615' to each side of the equation. -0.7283950615 + 0.7283950615 + x = -0.29345344 + 0.7283950615 Combine like terms: -0.7283950615 + 0.7283950615 = 0.0000000000 0.0000000000 + x = -0.29345344 + 0.7283950615 x = -0.29345344 + 0.7283950615 Combine like terms: -0.29345344 + 0.7283950615 = 0.4349416215 x = 0.4349416215 Simplifying x = 0.4349416215Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0218485015, 0.4349416215}
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