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Simplifying 9x2 + 4x + -45 = 0 Reorder the terms: -45 + 4x + 9x2 = 0 Solving -45 + 4x + 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'. -5 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 0.4444444444x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 0.4444444444x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 0.4444444444x + x2 = 0 + 5 0.4444444444x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 0.4444444444x + x2 = 5 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 5 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 5 + 0.04938271604 Combine like terms: 5 + 0.04938271604 = 5.04938271604 0.04938271604 + 0.4444444444x + x2 = 5.04938271604 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 5.04938271604 Calculate the square root of the right side: 2.247083157 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 2.247083157 and -2.247083157.Subproblem 1
x + 0.2222222222 = 2.247083157 Simplifying x + 0.2222222222 = 2.247083157 Reorder the terms: 0.2222222222 + x = 2.247083157 Solving 0.2222222222 + x = 2.247083157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 2.247083157 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 2.247083157 + -0.2222222222 x = 2.247083157 + -0.2222222222 Combine like terms: 2.247083157 + -0.2222222222 = 2.0248609348 x = 2.0248609348 Simplifying x = 2.0248609348Subproblem 2
x + 0.2222222222 = -2.247083157 Simplifying x + 0.2222222222 = -2.247083157 Reorder the terms: 0.2222222222 + x = -2.247083157 Solving 0.2222222222 + x = -2.247083157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -2.247083157 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -2.247083157 + -0.2222222222 x = -2.247083157 + -0.2222222222 Combine like terms: -2.247083157 + -0.2222222222 = -2.4693053792 x = -2.4693053792 Simplifying x = -2.4693053792Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0248609348, -2.4693053792}
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