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Simplifying 9x2 + 13x + -4 = 0 Reorder the terms: -4 + 13x + 9x2 = 0 Solving -4 + 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'. -0.4444444444 + 1.444444444x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 1.444444444x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 1.444444444x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 1.444444444x + x2 = 0 + 0.4444444444 1.444444444x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 1.444444444x + x2 = 0.4444444444 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 = 0.4444444444 + 0.5216049380 Reorder the terms: 0.5216049380 + 1.444444444x + x2 = 0.4444444444 + 0.5216049380 Combine like terms: 0.4444444444 + 0.5216049380 = 0.9660493824 0.5216049380 + 1.444444444x + x2 = 0.9660493824 Factor a perfect square on the left side: (x + 0.722222222)(x + 0.722222222) = 0.9660493824 Calculate the square root of the right side: 0.982878112 Break this problem into two subproblems by setting (x + 0.722222222) equal to 0.982878112 and -0.982878112.Subproblem 1
x + 0.722222222 = 0.982878112 Simplifying x + 0.722222222 = 0.982878112 Reorder the terms: 0.722222222 + x = 0.982878112 Solving 0.722222222 + x = 0.982878112 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 = 0.982878112 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = 0.982878112 + -0.722222222 x = 0.982878112 + -0.722222222 Combine like terms: 0.982878112 + -0.722222222 = 0.26065589 x = 0.26065589 Simplifying x = 0.26065589Subproblem 2
x + 0.722222222 = -0.982878112 Simplifying x + 0.722222222 = -0.982878112 Reorder the terms: 0.722222222 + x = -0.982878112 Solving 0.722222222 + x = -0.982878112 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 = -0.982878112 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = -0.982878112 + -0.722222222 x = -0.982878112 + -0.722222222 Combine like terms: -0.982878112 + -0.722222222 = -1.705100334 x = -1.705100334 Simplifying x = -1.705100334Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.26065589, -1.705100334}
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