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Simplifying 4x + 60 = 144x2 + 44 Reorder the terms: 60 + 4x = 144x2 + 44 Reorder the terms: 60 + 4x = 44 + 144x2 Solving 60 + 4x = 44 + 144x2 Solving for variable 'x'. Reorder the terms: 60 + -44 + 4x + -144x2 = 44 + 144x2 + -44 + -144x2 Combine like terms: 60 + -44 = 16 16 + 4x + -144x2 = 44 + 144x2 + -44 + -144x2 Reorder the terms: 16 + 4x + -144x2 = 44 + -44 + 144x2 + -144x2 Combine like terms: 44 + -44 = 0 16 + 4x + -144x2 = 0 + 144x2 + -144x2 16 + 4x + -144x2 = 144x2 + -144x2 Combine like terms: 144x2 + -144x2 = 0 16 + 4x + -144x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(4 + x + -36x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + x + -36x2)' equal to zero and attempt to solve: Simplifying 4 + x + -36x2 = 0 Solving 4 + x + -36x2 = 0 Begin completing the square. Divide all terms by -36 the coefficient of the squared term: Divide each side by '-36'. -0.1111111111 + -0.02777777778x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.02777777778x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.02777777778x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.02777777778x + x2 = 0 + 0.1111111111 -0.02777777778x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.02777777778x + x2 = 0.1111111111 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.02777777778x + 0.25 + x2 = 0.1111111111 + 0.25 Reorder the terms: 0.25 + -0.02777777778x + x2 = 0.1111111111 + 0.25 Combine like terms: 0.1111111111 + 0.25 = 0.3611111111 0.25 + -0.02777777778x + x2 = 0.3611111111 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.3611111111 Calculate the square root of the right side: 0.600925213 Break this problem into two subproblems by setting (x + 0.5) equal to 0.600925213 and -0.600925213.Subproblem 1
x + 0.5 = 0.600925213 Simplifying x + 0.5 = 0.600925213 Reorder the terms: 0.5 + x = 0.600925213 Solving 0.5 + x = 0.600925213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.600925213 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.600925213 + -0.5 x = 0.600925213 + -0.5 Combine like terms: 0.600925213 + -0.5 = 0.100925213 x = 0.100925213 Simplifying x = 0.100925213Subproblem 2
x + 0.5 = -0.600925213 Simplifying x + 0.5 = -0.600925213 Reorder the terms: 0.5 + x = -0.600925213 Solving 0.5 + x = -0.600925213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.600925213 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.600925213 + -0.5 x = -0.600925213 + -0.5 Combine like terms: -0.600925213 + -0.5 = -1.100925213 x = -1.100925213 Simplifying x = -1.100925213Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.100925213, -1.100925213}Solution
x = {0.100925213, -1.100925213}
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