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Simplifying 45x2 + -56x + 2 = 0 Reorder the terms: 2 + -56x + 45x2 = 0 Solving 2 + -56x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. 0.04444444444 + -1.244444444x + x2 = 0 Move the constant term to the right: Add '-0.04444444444' to each side of the equation. 0.04444444444 + -1.244444444x + -0.04444444444 + x2 = 0 + -0.04444444444 Reorder the terms: 0.04444444444 + -0.04444444444 + -1.244444444x + x2 = 0 + -0.04444444444 Combine like terms: 0.04444444444 + -0.04444444444 = 0.00000000000 0.00000000000 + -1.244444444x + x2 = 0 + -0.04444444444 -1.244444444x + x2 = 0 + -0.04444444444 Combine like terms: 0 + -0.04444444444 = -0.04444444444 -1.244444444x + x2 = -0.04444444444 The x term is -1.244444444x. Take half its coefficient (-0.622222222). Square it (0.3871604936) and add it to both sides. Add '0.3871604936' to each side of the equation. -1.244444444x + 0.3871604936 + x2 = -0.04444444444 + 0.3871604936 Reorder the terms: 0.3871604936 + -1.244444444x + x2 = -0.04444444444 + 0.3871604936 Combine like terms: -0.04444444444 + 0.3871604936 = 0.34271604916 0.3871604936 + -1.244444444x + x2 = 0.34271604916 Factor a perfect square on the left side: (x + -0.622222222)(x + -0.622222222) = 0.34271604916 Calculate the square root of the right side: 0.58541955 Break this problem into two subproblems by setting (x + -0.622222222) equal to 0.58541955 and -0.58541955.Subproblem 1
x + -0.622222222 = 0.58541955 Simplifying x + -0.622222222 = 0.58541955 Reorder the terms: -0.622222222 + x = 0.58541955 Solving -0.622222222 + x = 0.58541955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.622222222' to each side of the equation. -0.622222222 + 0.622222222 + x = 0.58541955 + 0.622222222 Combine like terms: -0.622222222 + 0.622222222 = 0.000000000 0.000000000 + x = 0.58541955 + 0.622222222 x = 0.58541955 + 0.622222222 Combine like terms: 0.58541955 + 0.622222222 = 1.207641772 x = 1.207641772 Simplifying x = 1.207641772Subproblem 2
x + -0.622222222 = -0.58541955 Simplifying x + -0.622222222 = -0.58541955 Reorder the terms: -0.622222222 + x = -0.58541955 Solving -0.622222222 + x = -0.58541955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.622222222' to each side of the equation. -0.622222222 + 0.622222222 + x = -0.58541955 + 0.622222222 Combine like terms: -0.622222222 + 0.622222222 = 0.000000000 0.000000000 + x = -0.58541955 + 0.622222222 x = -0.58541955 + 0.622222222 Combine like terms: -0.58541955 + 0.622222222 = 0.036802672 x = 0.036802672 Simplifying x = 0.036802672Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.207641772, 0.036802672}
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