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Simplifying 81x2 + 72x + 13 = 0 Reorder the terms: 13 + 72x + 81x2 = 0 Solving 13 + 72x + 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'. 0.1604938272 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '-0.1604938272' to each side of the equation. 0.1604938272 + 0.8888888889x + -0.1604938272 + x2 = 0 + -0.1604938272 Reorder the terms: 0.1604938272 + -0.1604938272 + 0.8888888889x + x2 = 0 + -0.1604938272 Combine like terms: 0.1604938272 + -0.1604938272 = 0.0000000000 0.0000000000 + 0.8888888889x + x2 = 0 + -0.1604938272 0.8888888889x + x2 = 0 + -0.1604938272 Combine like terms: 0 + -0.1604938272 = -0.1604938272 0.8888888889x + x2 = -0.1604938272 The x term is 0.8888888889x. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x + 0.1975308642 + x2 = -0.1604938272 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = -0.1604938272 + 0.1975308642 Combine like terms: -0.1604938272 + 0.1975308642 = 0.037037037 0.1975308642 + 0.8888888889x + x2 = 0.037037037 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 0.037037037 Calculate the square root of the right side: 0.19245009 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 0.19245009 and -0.19245009.Subproblem 1
x + 0.4444444445 = 0.19245009 Simplifying x + 0.4444444445 = 0.19245009 Reorder the terms: 0.4444444445 + x = 0.19245009 Solving 0.4444444445 + x = 0.19245009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 0.19245009 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 0.19245009 + -0.4444444445 x = 0.19245009 + -0.4444444445 Combine like terms: 0.19245009 + -0.4444444445 = -0.2519943545 x = -0.2519943545 Simplifying x = -0.2519943545Subproblem 2
x + 0.4444444445 = -0.19245009 Simplifying x + 0.4444444445 = -0.19245009 Reorder the terms: 0.4444444445 + x = -0.19245009 Solving 0.4444444445 + x = -0.19245009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -0.19245009 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -0.19245009 + -0.4444444445 x = -0.19245009 + -0.4444444445 Combine like terms: -0.19245009 + -0.4444444445 = -0.6368945345 x = -0.6368945345 Simplifying x = -0.6368945345Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2519943545, -0.6368945345}
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