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Simplifying (12y)(12y) + 40y = 7 Remove parenthesis around (12y) 12y(12y) + 40y = 7 Remove parenthesis around (12y) 12y * 12y + 40y = 7 Reorder the terms for easier multiplication: 12 * 12y * y + 40y = 7 Multiply 12 * 12 144y * y + 40y = 7 Multiply y * y 144y2 + 40y = 7 Reorder the terms: 40y + 144y2 = 7 Solving 40y + 144y2 = 7 Solving for variable 'y'. Reorder the terms: -7 + 40y + 144y2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 40y + 144y2 = 0 Begin completing the square. Divide all terms by 144 the coefficient of the squared term: Divide each side by '144'. -0.04861111111 + 0.2777777778y + y2 = 0 Move the constant term to the right: Add '0.04861111111' to each side of the equation. -0.04861111111 + 0.2777777778y + 0.04861111111 + y2 = 0 + 0.04861111111 Reorder the terms: -0.04861111111 + 0.04861111111 + 0.2777777778y + y2 = 0 + 0.04861111111 Combine like terms: -0.04861111111 + 0.04861111111 = 0.00000000000 0.00000000000 + 0.2777777778y + y2 = 0 + 0.04861111111 0.2777777778y + y2 = 0 + 0.04861111111 Combine like terms: 0 + 0.04861111111 = 0.04861111111 0.2777777778y + y2 = 0.04861111111 The y term is 0.2777777778y. Take half its coefficient (0.1388888889). Square it (0.01929012346) and add it to both sides. Add '0.01929012346' to each side of the equation. 0.2777777778y + 0.01929012346 + y2 = 0.04861111111 + 0.01929012346 Reorder the terms: 0.01929012346 + 0.2777777778y + y2 = 0.04861111111 + 0.01929012346 Combine like terms: 0.04861111111 + 0.01929012346 = 0.06790123457 0.01929012346 + 0.2777777778y + y2 = 0.06790123457 Factor a perfect square on the left side: (y + 0.1388888889)(y + 0.1388888889) = 0.06790123457 Calculate the square root of the right side: 0.260578653 Break this problem into two subproblems by setting (y + 0.1388888889) equal to 0.260578653 and -0.260578653.Subproblem 1
y + 0.1388888889 = 0.260578653 Simplifying y + 0.1388888889 = 0.260578653 Reorder the terms: 0.1388888889 + y = 0.260578653 Solving 0.1388888889 + y = 0.260578653 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.1388888889 + y = 0.260578653 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + y = 0.260578653 + -0.1388888889 y = 0.260578653 + -0.1388888889 Combine like terms: 0.260578653 + -0.1388888889 = 0.1216897641 y = 0.1216897641 Simplifying y = 0.1216897641Subproblem 2
y + 0.1388888889 = -0.260578653 Simplifying y + 0.1388888889 = -0.260578653 Reorder the terms: 0.1388888889 + y = -0.260578653 Solving 0.1388888889 + y = -0.260578653 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.1388888889 + y = -0.260578653 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + y = -0.260578653 + -0.1388888889 y = -0.260578653 + -0.1388888889 Combine like terms: -0.260578653 + -0.1388888889 = -0.3994675419 y = -0.3994675419 Simplifying y = -0.3994675419Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.1216897641, -0.3994675419}
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