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Simplifying 45x2 + -49x + 12.25 = 0 Reorder the terms: 12.25 + -49x + 45x2 = 0 Solving 12.25 + -49x + 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'. 0.2722222222 + -1.088888889x + x2 = 0 Move the constant term to the right: Add '-0.2722222222' to each side of the equation. 0.2722222222 + -1.088888889x + -0.2722222222 + x2 = 0 + -0.2722222222 Reorder the terms: 0.2722222222 + -0.2722222222 + -1.088888889x + x2 = 0 + -0.2722222222 Combine like terms: 0.2722222222 + -0.2722222222 = 0.0000000000 0.0000000000 + -1.088888889x + x2 = 0 + -0.2722222222 -1.088888889x + x2 = 0 + -0.2722222222 Combine like terms: 0 + -0.2722222222 = -0.2722222222 -1.088888889x + x2 = -0.2722222222 The x term is -1.088888889x. Take half its coefficient (-0.5444444445). Square it (0.2964197531) and add it to both sides. Add '0.2964197531' to each side of the equation. -1.088888889x + 0.2964197531 + x2 = -0.2722222222 + 0.2964197531 Reorder the terms: 0.2964197531 + -1.088888889x + x2 = -0.2722222222 + 0.2964197531 Combine like terms: -0.2722222222 + 0.2964197531 = 0.0241975309 0.2964197531 + -1.088888889x + x2 = 0.0241975309 Factor a perfect square on the left side: (x + -0.5444444445)(x + -0.5444444445) = 0.0241975309 Calculate the square root of the right side: 0.155555556 Break this problem into two subproblems by setting (x + -0.5444444445) equal to 0.155555556 and -0.155555556.Subproblem 1
x + -0.5444444445 = 0.155555556 Simplifying x + -0.5444444445 = 0.155555556 Reorder the terms: -0.5444444445 + x = 0.155555556 Solving -0.5444444445 + x = 0.155555556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5444444445' to each side of the equation. -0.5444444445 + 0.5444444445 + x = 0.155555556 + 0.5444444445 Combine like terms: -0.5444444445 + 0.5444444445 = 0.0000000000 0.0000000000 + x = 0.155555556 + 0.5444444445 x = 0.155555556 + 0.5444444445 Combine like terms: 0.155555556 + 0.5444444445 = 0.7000000005 x = 0.7000000005 Simplifying x = 0.7000000005Subproblem 2
x + -0.5444444445 = -0.155555556 Simplifying x + -0.5444444445 = -0.155555556 Reorder the terms: -0.5444444445 + x = -0.155555556 Solving -0.5444444445 + x = -0.155555556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5444444445' to each side of the equation. -0.5444444445 + 0.5444444445 + x = -0.155555556 + 0.5444444445 Combine like terms: -0.5444444445 + 0.5444444445 = 0.0000000000 0.0000000000 + x = -0.155555556 + 0.5444444445 x = -0.155555556 + 0.5444444445 Combine like terms: -0.155555556 + 0.5444444445 = 0.3888888885 x = 0.3888888885 Simplifying x = 0.3888888885Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7000000005, 0.3888888885}
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