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Simplifying 36x2 = 26x + 5 Reorder the terms: 36x2 = 5 + 26x Solving 36x2 = 5 + 26x Solving for variable 'x'. Reorder the terms: -5 + -26x + 36x2 = 5 + 26x + -5 + -26x Reorder the terms: -5 + -26x + 36x2 = 5 + -5 + 26x + -26x Combine like terms: 5 + -5 = 0 -5 + -26x + 36x2 = 0 + 26x + -26x -5 + -26x + 36x2 = 26x + -26x Combine like terms: 26x + -26x = 0 -5 + -26x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.1388888889 + -0.7222222222x + x2 = 0 Move the constant term to the right: Add '0.1388888889' to each side of the equation. -0.1388888889 + -0.7222222222x + 0.1388888889 + x2 = 0 + 0.1388888889 Reorder the terms: -0.1388888889 + 0.1388888889 + -0.7222222222x + x2 = 0 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + -0.7222222222x + x2 = 0 + 0.1388888889 -0.7222222222x + x2 = 0 + 0.1388888889 Combine like terms: 0 + 0.1388888889 = 0.1388888889 -0.7222222222x + x2 = 0.1388888889 The x term is -0.7222222222x. Take half its coefficient (-0.3611111111). Square it (0.1304012346) and add it to both sides. Add '0.1304012346' to each side of the equation. -0.7222222222x + 0.1304012346 + x2 = 0.1388888889 + 0.1304012346 Reorder the terms: 0.1304012346 + -0.7222222222x + x2 = 0.1388888889 + 0.1304012346 Combine like terms: 0.1388888889 + 0.1304012346 = 0.2692901235 0.1304012346 + -0.7222222222x + x2 = 0.2692901235 Factor a perfect square on the left side: (x + -0.3611111111)(x + -0.3611111111) = 0.2692901235 Calculate the square root of the right side: 0.518931714 Break this problem into two subproblems by setting (x + -0.3611111111) equal to 0.518931714 and -0.518931714.Subproblem 1
x + -0.3611111111 = 0.518931714 Simplifying x + -0.3611111111 = 0.518931714 Reorder the terms: -0.3611111111 + x = 0.518931714 Solving -0.3611111111 + x = 0.518931714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3611111111' to each side of the equation. -0.3611111111 + 0.3611111111 + x = 0.518931714 + 0.3611111111 Combine like terms: -0.3611111111 + 0.3611111111 = 0.0000000000 0.0000000000 + x = 0.518931714 + 0.3611111111 x = 0.518931714 + 0.3611111111 Combine like terms: 0.518931714 + 0.3611111111 = 0.8800428251 x = 0.8800428251 Simplifying x = 0.8800428251Subproblem 2
x + -0.3611111111 = -0.518931714 Simplifying x + -0.3611111111 = -0.518931714 Reorder the terms: -0.3611111111 + x = -0.518931714 Solving -0.3611111111 + x = -0.518931714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3611111111' to each side of the equation. -0.3611111111 + 0.3611111111 + x = -0.518931714 + 0.3611111111 Combine like terms: -0.3611111111 + 0.3611111111 = 0.0000000000 0.0000000000 + x = -0.518931714 + 0.3611111111 x = -0.518931714 + 0.3611111111 Combine like terms: -0.518931714 + 0.3611111111 = -0.1578206029 x = -0.1578206029 Simplifying x = -0.1578206029Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8800428251, -0.1578206029}
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