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Simplifying 9 + 51y + -51y2 = 0 Solving 9 + 51y + -51y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + 17y + -17y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 17y + -17y2)' equal to zero and attempt to solve: Simplifying 3 + 17y + -17y2 = 0 Solving 3 + 17y + -17y2 = 0 Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. -0.1764705882 + -1y + y2 = 0 Move the constant term to the right: Add '0.1764705882' to each side of the equation. -0.1764705882 + -1y + 0.1764705882 + y2 = 0 + 0.1764705882 Reorder the terms: -0.1764705882 + 0.1764705882 + -1y + y2 = 0 + 0.1764705882 Combine like terms: -0.1764705882 + 0.1764705882 = 0.0000000000 0.0000000000 + -1y + y2 = 0 + 0.1764705882 -1y + y2 = 0 + 0.1764705882 Combine like terms: 0 + 0.1764705882 = 0.1764705882 -1y + y2 = 0.1764705882 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 0.1764705882 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 0.1764705882 + 0.25 Combine like terms: 0.1764705882 + 0.25 = 0.4264705882 0.25 + -1y + y2 = 0.4264705882 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 0.4264705882 Calculate the square root of the right side: 0.653047156 Break this problem into two subproblems by setting (y + -0.5) equal to 0.653047156 and -0.653047156.Subproblem 1
y + -0.5 = 0.653047156 Simplifying y + -0.5 = 0.653047156 Reorder the terms: -0.5 + y = 0.653047156 Solving -0.5 + y = 0.653047156 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 0.653047156 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 0.653047156 + 0.5 y = 0.653047156 + 0.5 Combine like terms: 0.653047156 + 0.5 = 1.153047156 y = 1.153047156 Simplifying y = 1.153047156Subproblem 2
y + -0.5 = -0.653047156 Simplifying y + -0.5 = -0.653047156 Reorder the terms: -0.5 + y = -0.653047156 Solving -0.5 + y = -0.653047156 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -0.653047156 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -0.653047156 + 0.5 y = -0.653047156 + 0.5 Combine like terms: -0.653047156 + 0.5 = -0.153047156 y = -0.153047156 Simplifying y = -0.153047156Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.153047156, -0.153047156}Solution
y = {1.153047156, -0.153047156}
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