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Simplifying 9x2 + 13x + -2 = 0 Reorder the terms: -2 + 13x + 9x2 = 0 Solving -2 + 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'. -0.2222222222 + 1.444444444x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 1.444444444x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 1.444444444x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 1.444444444x + x2 = 0 + 0.2222222222 1.444444444x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 1.444444444x + x2 = 0.2222222222 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 = 0.2222222222 + 0.5216049380 Reorder the terms: 0.5216049380 + 1.444444444x + x2 = 0.2222222222 + 0.5216049380 Combine like terms: 0.2222222222 + 0.5216049380 = 0.7438271602 0.5216049380 + 1.444444444x + x2 = 0.7438271602 Factor a perfect square on the left side: (x + 0.722222222)(x + 0.722222222) = 0.7438271602 Calculate the square root of the right side: 0.86245415 Break this problem into two subproblems by setting (x + 0.722222222) equal to 0.86245415 and -0.86245415.Subproblem 1
x + 0.722222222 = 0.86245415 Simplifying x + 0.722222222 = 0.86245415 Reorder the terms: 0.722222222 + x = 0.86245415 Solving 0.722222222 + x = 0.86245415 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 = 0.86245415 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = 0.86245415 + -0.722222222 x = 0.86245415 + -0.722222222 Combine like terms: 0.86245415 + -0.722222222 = 0.140231928 x = 0.140231928 Simplifying x = 0.140231928Subproblem 2
x + 0.722222222 = -0.86245415 Simplifying x + 0.722222222 = -0.86245415 Reorder the terms: 0.722222222 + x = -0.86245415 Solving 0.722222222 + x = -0.86245415 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 = -0.86245415 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = -0.86245415 + -0.722222222 x = -0.86245415 + -0.722222222 Combine like terms: -0.86245415 + -0.722222222 = -1.584676372 x = -1.584676372 Simplifying x = -1.584676372Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.140231928, -1.584676372}
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