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Simplifying 9x2 + 13x + 1 = 0 Reorder the terms: 1 + 13x + 9x2 = 0 Solving 1 + 13x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + 1.444444444x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 1.444444444x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 1.444444444x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 1.444444444x + x2 = 0 + -0.1111111111 1.444444444x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 1.444444444x + x2 = -0.1111111111 The x term is 1.444444444x. Take half its coefficient (0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. 1.444444444x + 0.5216049380 + x2 = -0.1111111111 + 0.5216049380 Reorder the terms: 0.5216049380 + 1.444444444x + x2 = -0.1111111111 + 0.5216049380 Combine like terms: -0.1111111111 + 0.5216049380 = 0.4104938269 0.5216049380 + 1.444444444x + x2 = 0.4104938269 Factor a perfect square on the left side: (x + 0.722222222)(x + 0.722222222) = 0.4104938269 Calculate the square root of the right side: 0.640697922 Break this problem into two subproblems by setting (x + 0.722222222) equal to 0.640697922 and -0.640697922.Subproblem 1
x + 0.722222222 = 0.640697922 Simplifying x + 0.722222222 = 0.640697922 Reorder the terms: 0.722222222 + x = 0.640697922 Solving 0.722222222 + x = 0.640697922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + x = 0.640697922 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = 0.640697922 + -0.722222222 x = 0.640697922 + -0.722222222 Combine like terms: 0.640697922 + -0.722222222 = -0.0815243 x = -0.0815243 Simplifying x = -0.0815243Subproblem 2
x + 0.722222222 = -0.640697922 Simplifying x + 0.722222222 = -0.640697922 Reorder the terms: 0.722222222 + x = -0.640697922 Solving 0.722222222 + x = -0.640697922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + x = -0.640697922 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = -0.640697922 + -0.722222222 x = -0.640697922 + -0.722222222 Combine like terms: -0.640697922 + -0.722222222 = -1.362920144 x = -1.362920144 Simplifying x = -1.362920144Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0815243, -1.362920144}
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