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Simplifying 0 = 17y2 + 144y + 286 Reorder the terms: 0 = 286 + 144y + 17y2 Solving 0 = 286 + 144y + 17y2 Solving for variable 'y'. Combine like terms: 0 + -286 = -286 -286 + -144y + -17y2 = 286 + 144y + 17y2 + -286 + -144y + -17y2 Reorder the terms: -286 + -144y + -17y2 = 286 + -286 + 144y + -144y + 17y2 + -17y2 Combine like terms: 286 + -286 = 0 -286 + -144y + -17y2 = 0 + 144y + -144y + 17y2 + -17y2 -286 + -144y + -17y2 = 144y + -144y + 17y2 + -17y2 Combine like terms: 144y + -144y = 0 -286 + -144y + -17y2 = 0 + 17y2 + -17y2 -286 + -144y + -17y2 = 17y2 + -17y2 Combine like terms: 17y2 + -17y2 = 0 -286 + -144y + -17y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(286 + 144y + 17y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(286 + 144y + 17y2)' equal to zero and attempt to solve: Simplifying 286 + 144y + 17y2 = 0 Solving 286 + 144y + 17y2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 16.82352941 + 8.470588235y + y2 = 0 Move the constant term to the right: Add '-16.82352941' to each side of the equation. 16.82352941 + 8.470588235y + -16.82352941 + y2 = 0 + -16.82352941 Reorder the terms: 16.82352941 + -16.82352941 + 8.470588235y + y2 = 0 + -16.82352941 Combine like terms: 16.82352941 + -16.82352941 = 0.00000000 0.00000000 + 8.470588235y + y2 = 0 + -16.82352941 8.470588235y + y2 = 0 + -16.82352941 Combine like terms: 0 + -16.82352941 = -16.82352941 8.470588235y + y2 = -16.82352941 The y term is 8.470588235y. Take half its coefficient (4.235294118). Square it (17.93771627) and add it to both sides. Add '17.93771627' to each side of the equation. 8.470588235y + 17.93771627 + y2 = -16.82352941 + 17.93771627 Reorder the terms: 17.93771627 + 8.470588235y + y2 = -16.82352941 + 17.93771627 Combine like terms: -16.82352941 + 17.93771627 = 1.11418686 17.93771627 + 8.470588235y + y2 = 1.11418686 Factor a perfect square on the left side: (y + 4.235294118)(y + 4.235294118) = 1.11418686 Calculate the square root of the right side: 1.055550501 Break this problem into two subproblems by setting (y + 4.235294118) equal to 1.055550501 and -1.055550501.Subproblem 1
y + 4.235294118 = 1.055550501 Simplifying y + 4.235294118 = 1.055550501 Reorder the terms: 4.235294118 + y = 1.055550501 Solving 4.235294118 + y = 1.055550501 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.235294118' to each side of the equation. 4.235294118 + -4.235294118 + y = 1.055550501 + -4.235294118 Combine like terms: 4.235294118 + -4.235294118 = 0.000000000 0.000000000 + y = 1.055550501 + -4.235294118 y = 1.055550501 + -4.235294118 Combine like terms: 1.055550501 + -4.235294118 = -3.179743617 y = -3.179743617 Simplifying y = -3.179743617Subproblem 2
y + 4.235294118 = -1.055550501 Simplifying y + 4.235294118 = -1.055550501 Reorder the terms: 4.235294118 + y = -1.055550501 Solving 4.235294118 + y = -1.055550501 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.235294118' to each side of the equation. 4.235294118 + -4.235294118 + y = -1.055550501 + -4.235294118 Combine like terms: 4.235294118 + -4.235294118 = 0.000000000 0.000000000 + y = -1.055550501 + -4.235294118 y = -1.055550501 + -4.235294118 Combine like terms: -1.055550501 + -4.235294118 = -5.290844619 y = -5.290844619 Simplifying y = -5.290844619Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.179743617, -5.290844619}Solution
y = {-3.179743617, -5.290844619}
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