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Simplifying (-7y4 + 14 + -2y2) + -1(5 + -6y4) = 0 Reorder the terms: (14 + -2y2 + -7y4) + -1(5 + -6y4) = 0 Remove parenthesis around (14 + -2y2 + -7y4) 14 + -2y2 + -7y4 + -1(5 + -6y4) = 0 14 + -2y2 + -7y4 + (5 * -1 + -6y4 * -1) = 0 14 + -2y2 + -7y4 + (-5 + 6y4) = 0 Reorder the terms: 14 + -5 + -2y2 + -7y4 + 6y4 = 0 Combine like terms: 14 + -5 = 9 9 + -2y2 + -7y4 + 6y4 = 0 Combine like terms: -7y4 + 6y4 = -1y4 9 + -2y2 + -1y4 = 0 Solving 9 + -2y2 + -1y4 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 2y2 + y4 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 2y2 + 9 + y4 = 0 + 9 Reorder the terms: -9 + 9 + 2y2 + y4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2y2 + y4 = 0 + 9 2y2 + y4 = 0 + 9 Combine like terms: 0 + 9 = 9 2y2 + y4 = 9 The y term is 2y2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y2 + 1 + y4 = 9 + 1 Reorder the terms: 1 + 2y2 + y4 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + 2y2 + y4 = 10 Factor a perfect square on the left side: (y2 + 1)(y2 + 1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (y2 + 1) equal to 3.16227766 and -3.16227766.Subproblem 1
y2 + 1 = 3.16227766 Simplifying y2 + 1 = 3.16227766 Reorder the terms: 1 + y2 = 3.16227766 Solving 1 + y2 = 3.16227766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y2 = 3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = 3.16227766 + -1 y2 = 3.16227766 + -1 Combine like terms: 3.16227766 + -1 = 2.16227766 y2 = 2.16227766 Simplifying y2 = 2.16227766 Take the square root of each side: y = {-1.470468517, 1.470468517}Subproblem 2
y2 + 1 = -3.16227766 Simplifying y2 + 1 = -3.16227766 Reorder the terms: 1 + y2 = -3.16227766 Solving 1 + y2 = -3.16227766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y2 = -3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = -3.16227766 + -1 y2 = -3.16227766 + -1 Combine like terms: -3.16227766 + -1 = -4.16227766 y2 = -4.16227766 Simplifying y2 = -4.16227766 Reorder the terms: 4.16227766 + y2 = -4.16227766 + 4.16227766 Combine like terms: -4.16227766 + 4.16227766 = 0.00000000 4.16227766 + y2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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