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Simplifying 4(y + 10) * y = 5 Reorder the terms: 4(10 + y) * y = 5 Reorder the terms for easier multiplication: 4y(10 + y) = 5 (10 * 4y + y * 4y) = 5 (40y + 4y2) = 5 Solving 40y + 4y2 = 5 Solving for variable 'y'. Reorder the terms: -5 + 40y + 4y2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 40y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 10y + y2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 10y + 1.25 + y2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 10y + y2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 10y + y2 = 0 + 1.25 10y + y2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 10y + y2 = 1.25 The y term is 10y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10y + 25 + y2 = 1.25 + 25 Reorder the terms: 25 + 10y + y2 = 1.25 + 25 Combine like terms: 1.25 + 25 = 26.25 25 + 10y + y2 = 26.25 Factor a perfect square on the left side: (y + 5)(y + 5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (y + 5) equal to 5.123475383 and -5.123475383.Subproblem 1
y + 5 = 5.123475383 Simplifying y + 5 = 5.123475383 Reorder the terms: 5 + y = 5.123475383 Solving 5 + y = 5.123475383 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 5.123475383 + -5 Combine like terms: 5 + -5 = 0 0 + y = 5.123475383 + -5 y = 5.123475383 + -5 Combine like terms: 5.123475383 + -5 = 0.123475383 y = 0.123475383 Simplifying y = 0.123475383Subproblem 2
y + 5 = -5.123475383 Simplifying y + 5 = -5.123475383 Reorder the terms: 5 + y = -5.123475383 Solving 5 + y = -5.123475383 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = -5.123475383 + -5 Combine like terms: 5 + -5 = 0 0 + y = -5.123475383 + -5 y = -5.123475383 + -5 Combine like terms: -5.123475383 + -5 = -10.123475383 y = -10.123475383 Simplifying y = -10.123475383Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.123475383, -10.123475383}
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