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Simplifying 9x2 = 4x + 2 Reorder the terms: 9x2 = 2 + 4x Solving 9x2 = 2 + 4x Solving for variable 'x'. Reorder the terms: -2 + -4x + 9x2 = 2 + 4x + -2 + -4x Reorder the terms: -2 + -4x + 9x2 = 2 + -2 + 4x + -4x Combine like terms: 2 + -2 = 0 -2 + -4x + 9x2 = 0 + 4x + -4x -2 + -4x + 9x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -2 + -4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -0.4444444444x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -0.4444444444x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -0.4444444444x + x2 = 0 + 0.2222222222 -0.4444444444x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -0.4444444444x + x2 = 0.2222222222 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 = 0.2222222222 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 0.2222222222 + 0.04938271604 Combine like terms: 0.2222222222 + 0.04938271604 = 0.27160493824 0.04938271604 + -0.4444444444x + x2 = 0.27160493824 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 0.27160493824 Calculate the square root of the right side: 0.521157307 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 0.521157307 and -0.521157307.Subproblem 1
x + -0.2222222222 = 0.521157307 Simplifying x + -0.2222222222 = 0.521157307 Reorder the terms: -0.2222222222 + x = 0.521157307 Solving -0.2222222222 + x = 0.521157307 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 = 0.521157307 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 0.521157307 + 0.2222222222 x = 0.521157307 + 0.2222222222 Combine like terms: 0.521157307 + 0.2222222222 = 0.7433795292 x = 0.7433795292 Simplifying x = 0.7433795292Subproblem 2
x + -0.2222222222 = -0.521157307 Simplifying x + -0.2222222222 = -0.521157307 Reorder the terms: -0.2222222222 + x = -0.521157307 Solving -0.2222222222 + x = -0.521157307 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 = -0.521157307 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -0.521157307 + 0.2222222222 x = -0.521157307 + 0.2222222222 Combine like terms: -0.521157307 + 0.2222222222 = -0.2989350848 x = -0.2989350848 Simplifying x = -0.2989350848Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7433795292, -0.2989350848}
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