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Simplifying -4y2 + 16y + 632 = 0 Reorder the terms: 632 + 16y + -4y2 = 0 Solving 632 + 16y + -4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(158 + 4y + -1y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(158 + 4y + -1y2)' equal to zero and attempt to solve: Simplifying 158 + 4y + -1y2 = 0 Solving 158 + 4y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -158 + -4y + y2 = 0 Move the constant term to the right: Add '158' to each side of the equation. -158 + -4y + 158 + y2 = 0 + 158 Reorder the terms: -158 + 158 + -4y + y2 = 0 + 158 Combine like terms: -158 + 158 = 0 0 + -4y + y2 = 0 + 158 -4y + y2 = 0 + 158 Combine like terms: 0 + 158 = 158 -4y + y2 = 158 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 = 158 + 4 Reorder the terms: 4 + -4y + y2 = 158 + 4 Combine like terms: 158 + 4 = 162 4 + -4y + y2 = 162 Factor a perfect square on the left side: (y + -2)(y + -2) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (y + -2) equal to 12.727922061 and -12.727922061.Subproblem 1
y + -2 = 12.727922061 Simplifying y + -2 = 12.727922061 Reorder the terms: -2 + y = 12.727922061 Solving -2 + y = 12.727922061 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 = 12.727922061 + 2 Combine like terms: -2 + 2 = 0 0 + y = 12.727922061 + 2 y = 12.727922061 + 2 Combine like terms: 12.727922061 + 2 = 14.727922061 y = 14.727922061 Simplifying y = 14.727922061Subproblem 2
y + -2 = -12.727922061 Simplifying y + -2 = -12.727922061 Reorder the terms: -2 + y = -12.727922061 Solving -2 + y = -12.727922061 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 = -12.727922061 + 2 Combine like terms: -2 + 2 = 0 0 + y = -12.727922061 + 2 y = -12.727922061 + 2 Combine like terms: -12.727922061 + 2 = -10.727922061 y = -10.727922061 Simplifying y = -10.727922061Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.727922061, -10.727922061}Solution
y = {14.727922061, -10.727922061}
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