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Simplifying 4x2 + 196x + 45 = 0 Reorder the terms: 45 + 196x + 4x2 = 0 Solving 45 + 196x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 11.25 + 49x + x2 = 0 Move the constant term to the right: Add '-11.25' to each side of the equation. 11.25 + 49x + -11.25 + x2 = 0 + -11.25 Reorder the terms: 11.25 + -11.25 + 49x + x2 = 0 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + 49x + x2 = 0 + -11.25 49x + x2 = 0 + -11.25 Combine like terms: 0 + -11.25 = -11.25 49x + x2 = -11.25 The x term is 49x. Take half its coefficient (24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. 49x + 600.25 + x2 = -11.25 + 600.25 Reorder the terms: 600.25 + 49x + x2 = -11.25 + 600.25 Combine like terms: -11.25 + 600.25 = 589 600.25 + 49x + x2 = 589 Factor a perfect square on the left side: (x + 24.5)(x + 24.5) = 589 Calculate the square root of the right side: 24.269322199 Break this problem into two subproblems by setting (x + 24.5) equal to 24.269322199 and -24.269322199.Subproblem 1
x + 24.5 = 24.269322199 Simplifying x + 24.5 = 24.269322199 Reorder the terms: 24.5 + x = 24.269322199 Solving 24.5 + x = 24.269322199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = 24.269322199 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 24.269322199 + -24.5 x = 24.269322199 + -24.5 Combine like terms: 24.269322199 + -24.5 = -0.230677801 x = -0.230677801 Simplifying x = -0.230677801Subproblem 2
x + 24.5 = -24.269322199 Simplifying x + 24.5 = -24.269322199 Reorder the terms: 24.5 + x = -24.269322199 Solving 24.5 + x = -24.269322199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = -24.269322199 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -24.269322199 + -24.5 x = -24.269322199 + -24.5 Combine like terms: -24.269322199 + -24.5 = -48.769322199 x = -48.769322199 Simplifying x = -48.769322199Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.230677801, -48.769322199}
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