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Simplifying 7(4 + -1y) * 9y + 20 = 0 Reorder the terms for easier multiplication: 7 * 9y(4 + -1y) + 20 = 0 Multiply 7 * 9 63y(4 + -1y) + 20 = 0 (4 * 63y + -1y * 63y) + 20 = 0 (252y + -63y2) + 20 = 0 Reorder the terms: 20 + 252y + -63y2 = 0 Solving 20 + 252y + -63y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -63 the coefficient of the squared term: Divide each side by '-63'. -0.3174603175 + -4y + y2 = 0 Move the constant term to the right: Add '0.3174603175' to each side of the equation. -0.3174603175 + -4y + 0.3174603175 + y2 = 0 + 0.3174603175 Reorder the terms: -0.3174603175 + 0.3174603175 + -4y + y2 = 0 + 0.3174603175 Combine like terms: -0.3174603175 + 0.3174603175 = 0.0000000000 0.0000000000 + -4y + y2 = 0 + 0.3174603175 -4y + y2 = 0 + 0.3174603175 Combine like terms: 0 + 0.3174603175 = 0.3174603175 -4y + y2 = 0.3174603175 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 0.3174603175 + 4 Reorder the terms: 4 + -4y + y2 = 0.3174603175 + 4 Combine like terms: 0.3174603175 + 4 = 4.3174603175 4 + -4y + y2 = 4.3174603175 Factor a perfect square on the left side: (y + -2)(y + -2) = 4.3174603175 Calculate the square root of the right side: 2.077849927 Break this problem into two subproblems by setting (y + -2) equal to 2.077849927 and -2.077849927.Subproblem 1
y + -2 = 2.077849927 Simplifying y + -2 = 2.077849927 Reorder the terms: -2 + y = 2.077849927 Solving -2 + y = 2.077849927 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 2.077849927 + 2 Combine like terms: -2 + 2 = 0 0 + y = 2.077849927 + 2 y = 2.077849927 + 2 Combine like terms: 2.077849927 + 2 = 4.077849927 y = 4.077849927 Simplifying y = 4.077849927Subproblem 2
y + -2 = -2.077849927 Simplifying y + -2 = -2.077849927 Reorder the terms: -2 + y = -2.077849927 Solving -2 + y = -2.077849927 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -2.077849927 + 2 Combine like terms: -2 + 2 = 0 0 + y = -2.077849927 + 2 y = -2.077849927 + 2 Combine like terms: -2.077849927 + 2 = -0.077849927 y = -0.077849927 Simplifying y = -0.077849927Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.077849927, -0.077849927}
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