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Simplifying -4y2 + 40y = 28 Reorder the terms: 40y + -4y2 = 28 Solving 40y + -4y2 = 28 Solving for variable 'y'. Reorder the terms: -28 + 40y + -4y2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 40y + -4y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + 10y + -1y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + 10y + -1y2)' equal to zero and attempt to solve: Simplifying -7 + 10y + -1y2 = 0 Solving -7 + 10y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -10y + y2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -10y + -7 + y2 = 0 + -7 Reorder the terms: 7 + -7 + -10y + y2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -10y + y2 = 0 + -7 -10y + y2 = 0 + -7 Combine like terms: 0 + -7 = -7 -10y + y2 = -7 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 = -7 + 25 Reorder the terms: 25 + -10y + y2 = -7 + 25 Combine like terms: -7 + 25 = 18 25 + -10y + y2 = 18 Factor a perfect square on the left side: (y + -5)(y + -5) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (y + -5) equal to 4.242640687 and -4.242640687.Subproblem 1
y + -5 = 4.242640687 Simplifying y + -5 = 4.242640687 Reorder the terms: -5 + y = 4.242640687 Solving -5 + y = 4.242640687 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 = 4.242640687 + 5 Combine like terms: -5 + 5 = 0 0 + y = 4.242640687 + 5 y = 4.242640687 + 5 Combine like terms: 4.242640687 + 5 = 9.242640687 y = 9.242640687 Simplifying y = 9.242640687Subproblem 2
y + -5 = -4.242640687 Simplifying y + -5 = -4.242640687 Reorder the terms: -5 + y = -4.242640687 Solving -5 + y = -4.242640687 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 = -4.242640687 + 5 Combine like terms: -5 + 5 = 0 0 + y = -4.242640687 + 5 y = -4.242640687 + 5 Combine like terms: -4.242640687 + 5 = 0.757359313 y = 0.757359313 Simplifying y = 0.757359313Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.242640687, 0.757359313}Solution
y = {9.242640687, 0.757359313}
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