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Simplifying -22x + -48 + 48x2 = 0 Reorder the terms: -48 + -22x + 48x2 = 0 Solving -48 + -22x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + -11x + 24x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-24 + -11x + 24x2)' equal to zero and attempt to solve: Simplifying -24 + -11x + 24x2 = 0 Solving -24 + -11x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -1 + -0.4583333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.4583333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.4583333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.4583333333x + x2 = 0 + 1 -0.4583333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.4583333333x + x2 = 1 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 = 1 + 0.05251736113 Reorder the terms: 0.05251736113 + -0.4583333333x + x2 = 1 + 0.05251736113 Combine like terms: 1 + 0.05251736113 = 1.05251736113 0.05251736113 + -0.4583333333x + x2 = 1.05251736113 Factor a perfect square on the left side: (x + -0.2291666667)(x + -0.2291666667) = 1.05251736113 Calculate the square root of the right side: 1.025922688 Break this problem into two subproblems by setting (x + -0.2291666667) equal to 1.025922688 and -1.025922688.Subproblem 1
x + -0.2291666667 = 1.025922688 Simplifying x + -0.2291666667 = 1.025922688 Reorder the terms: -0.2291666667 + x = 1.025922688 Solving -0.2291666667 + x = 1.025922688 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 = 1.025922688 + 0.2291666667 Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000 0.0000000000 + x = 1.025922688 + 0.2291666667 x = 1.025922688 + 0.2291666667 Combine like terms: 1.025922688 + 0.2291666667 = 1.2550893547 x = 1.2550893547 Simplifying x = 1.2550893547Subproblem 2
x + -0.2291666667 = -1.025922688 Simplifying x + -0.2291666667 = -1.025922688 Reorder the terms: -0.2291666667 + x = -1.025922688 Solving -0.2291666667 + x = -1.025922688 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 = -1.025922688 + 0.2291666667 Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000 0.0000000000 + x = -1.025922688 + 0.2291666667 x = -1.025922688 + 0.2291666667 Combine like terms: -1.025922688 + 0.2291666667 = -0.7967560213 x = -0.7967560213 Simplifying x = -0.7967560213Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2550893547, -0.7967560213}Solution
x = {1.2550893547, -0.7967560213}
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