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Simplifying 13y2 + 15y + -1 = 0 Reorder the terms: -1 + 15y + 13y2 = 0 Solving -1 + 15y + 13y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.07692307692 + 1.153846154y + y2 = 0 Move the constant term to the right: Add '0.07692307692' to each side of the equation. -0.07692307692 + 1.153846154y + 0.07692307692 + y2 = 0 + 0.07692307692 Reorder the terms: -0.07692307692 + 0.07692307692 + 1.153846154y + y2 = 0 + 0.07692307692 Combine like terms: -0.07692307692 + 0.07692307692 = 0.00000000000 0.00000000000 + 1.153846154y + y2 = 0 + 0.07692307692 1.153846154y + y2 = 0 + 0.07692307692 Combine like terms: 0 + 0.07692307692 = 0.07692307692 1.153846154y + y2 = 0.07692307692 The y term is 1.153846154y. Take half its coefficient (0.576923077). Square it (0.3328402368) and add it to both sides. Add '0.3328402368' to each side of the equation. 1.153846154y + 0.3328402368 + y2 = 0.07692307692 + 0.3328402368 Reorder the terms: 0.3328402368 + 1.153846154y + y2 = 0.07692307692 + 0.3328402368 Combine like terms: 0.07692307692 + 0.3328402368 = 0.40976331372 0.3328402368 + 1.153846154y + y2 = 0.40976331372 Factor a perfect square on the left side: (y + 0.576923077)(y + 0.576923077) = 0.40976331372 Calculate the square root of the right side: 0.640127576 Break this problem into two subproblems by setting (y + 0.576923077) equal to 0.640127576 and -0.640127576.Subproblem 1
y + 0.576923077 = 0.640127576 Simplifying y + 0.576923077 = 0.640127576 Reorder the terms: 0.576923077 + y = 0.640127576 Solving 0.576923077 + y = 0.640127576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.576923077' to each side of the equation. 0.576923077 + -0.576923077 + y = 0.640127576 + -0.576923077 Combine like terms: 0.576923077 + -0.576923077 = 0.000000000 0.000000000 + y = 0.640127576 + -0.576923077 y = 0.640127576 + -0.576923077 Combine like terms: 0.640127576 + -0.576923077 = 0.063204499 y = 0.063204499 Simplifying y = 0.063204499Subproblem 2
y + 0.576923077 = -0.640127576 Simplifying y + 0.576923077 = -0.640127576 Reorder the terms: 0.576923077 + y = -0.640127576 Solving 0.576923077 + y = -0.640127576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.576923077' to each side of the equation. 0.576923077 + -0.576923077 + y = -0.640127576 + -0.576923077 Combine like terms: 0.576923077 + -0.576923077 = 0.000000000 0.000000000 + y = -0.640127576 + -0.576923077 y = -0.640127576 + -0.576923077 Combine like terms: -0.640127576 + -0.576923077 = -1.217050653 y = -1.217050653 Simplifying y = -1.217050653Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.063204499, -1.217050653}
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