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Simplifying 48x2 + 22x + -25 = 0 Reorder the terms: -25 + 22x + 48x2 = 0 Solving -25 + 22x + 48x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.5208333333 + 0.4583333333x + x2 = 0 Move the constant term to the right: Add '0.5208333333' to each side of the equation. -0.5208333333 + 0.4583333333x + 0.5208333333 + x2 = 0 + 0.5208333333 Reorder the terms: -0.5208333333 + 0.5208333333 + 0.4583333333x + x2 = 0 + 0.5208333333 Combine like terms: -0.5208333333 + 0.5208333333 = 0.0000000000 0.0000000000 + 0.4583333333x + x2 = 0 + 0.5208333333 0.4583333333x + x2 = 0 + 0.5208333333 Combine like terms: 0 + 0.5208333333 = 0.5208333333 0.4583333333x + x2 = 0.5208333333 The x term is 0.4583333333x. Take half its coefficient (0.2291666667). Square it (0.05251736113) and add it to both sides. Add '0.05251736113' to each side of the equation. 0.4583333333x + 0.05251736113 + x2 = 0.5208333333 + 0.05251736113 Reorder the terms: 0.05251736113 + 0.4583333333x + x2 = 0.5208333333 + 0.05251736113 Combine like terms: 0.5208333333 + 0.05251736113 = 0.57335069443 0.05251736113 + 0.4583333333x + x2 = 0.57335069443 Factor a perfect square on the left side: (x + 0.2291666667)(x + 0.2291666667) = 0.57335069443 Calculate the square root of the right side: 0.757199244 Break this problem into two subproblems by setting (x + 0.2291666667) equal to 0.757199244 and -0.757199244.Subproblem 1
x + 0.2291666667 = 0.757199244 Simplifying x + 0.2291666667 = 0.757199244 Reorder the terms: 0.2291666667 + x = 0.757199244 Solving 0.2291666667 + x = 0.757199244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2291666667' to each side of the equation. 0.2291666667 + -0.2291666667 + x = 0.757199244 + -0.2291666667 Combine like terms: 0.2291666667 + -0.2291666667 = 0.0000000000 0.0000000000 + x = 0.757199244 + -0.2291666667 x = 0.757199244 + -0.2291666667 Combine like terms: 0.757199244 + -0.2291666667 = 0.5280325773 x = 0.5280325773 Simplifying x = 0.5280325773Subproblem 2
x + 0.2291666667 = -0.757199244 Simplifying x + 0.2291666667 = -0.757199244 Reorder the terms: 0.2291666667 + x = -0.757199244 Solving 0.2291666667 + x = -0.757199244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2291666667' to each side of the equation. 0.2291666667 + -0.2291666667 + x = -0.757199244 + -0.2291666667 Combine like terms: 0.2291666667 + -0.2291666667 = 0.0000000000 0.0000000000 + x = -0.757199244 + -0.2291666667 x = -0.757199244 + -0.2291666667 Combine like terms: -0.757199244 + -0.2291666667 = -0.9863659107 x = -0.9863659107 Simplifying x = -0.9863659107Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5280325773, -0.9863659107}
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