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Simplifying 0 = 3y2 + 30y + 70 Reorder the terms: 0 = 70 + 30y + 3y2 Solving 0 = 70 + 30y + 3y2 Solving for variable 'y'. Combine like terms: 0 + -70 = -70 -70 + -30y + -3y2 = 70 + 30y + 3y2 + -70 + -30y + -3y2 Reorder the terms: -70 + -30y + -3y2 = 70 + -70 + 30y + -30y + 3y2 + -3y2 Combine like terms: 70 + -70 = 0 -70 + -30y + -3y2 = 0 + 30y + -30y + 3y2 + -3y2 -70 + -30y + -3y2 = 30y + -30y + 3y2 + -3y2 Combine like terms: 30y + -30y = 0 -70 + -30y + -3y2 = 0 + 3y2 + -3y2 -70 + -30y + -3y2 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 -70 + -30y + -3y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(70 + 30y + 3y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(70 + 30y + 3y2)' equal to zero and attempt to solve: Simplifying 70 + 30y + 3y2 = 0 Solving 70 + 30y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 23.33333333 + 10y + y2 = 0 Move the constant term to the right: Add '-23.33333333' to each side of the equation. 23.33333333 + 10y + -23.33333333 + y2 = 0 + -23.33333333 Reorder the terms: 23.33333333 + -23.33333333 + 10y + y2 = 0 + -23.33333333 Combine like terms: 23.33333333 + -23.33333333 = 0.00000000 0.00000000 + 10y + y2 = 0 + -23.33333333 10y + y2 = 0 + -23.33333333 Combine like terms: 0 + -23.33333333 = -23.33333333 10y + y2 = -23.33333333 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 = -23.33333333 + 25 Reorder the terms: 25 + 10y + y2 = -23.33333333 + 25 Combine like terms: -23.33333333 + 25 = 1.66666667 25 + 10y + y2 = 1.66666667 Factor a perfect square on the left side: (y + 5)(y + 5) = 1.66666667 Calculate the square root of the right side: 1.29099445 Break this problem into two subproblems by setting (y + 5) equal to 1.29099445 and -1.29099445.Subproblem 1
y + 5 = 1.29099445 Simplifying y + 5 = 1.29099445 Reorder the terms: 5 + y = 1.29099445 Solving 5 + y = 1.29099445 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 = 1.29099445 + -5 Combine like terms: 5 + -5 = 0 0 + y = 1.29099445 + -5 y = 1.29099445 + -5 Combine like terms: 1.29099445 + -5 = -3.70900555 y = -3.70900555 Simplifying y = -3.70900555Subproblem 2
y + 5 = -1.29099445 Simplifying y + 5 = -1.29099445 Reorder the terms: 5 + y = -1.29099445 Solving 5 + y = -1.29099445 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 = -1.29099445 + -5 Combine like terms: 5 + -5 = 0 0 + y = -1.29099445 + -5 y = -1.29099445 + -5 Combine like terms: -1.29099445 + -5 = -6.29099445 y = -6.29099445 Simplifying y = -6.29099445Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.70900555, -6.29099445}Solution
y = {-3.70900555, -6.29099445}
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