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Simplifying 14y2 + 15y + -3 = 0 Reorder the terms: -3 + 15y + 14y2 = 0 Solving -3 + 15y + 14y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.2142857143 + 1.071428571y + y2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + 1.071428571y + 0.2142857143 + y2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + 1.071428571y + y2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + 1.071428571y + y2 = 0 + 0.2142857143 1.071428571y + y2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 1.071428571y + y2 = 0.2142857143 The y term is 1.071428571y. Take half its coefficient (0.5357142855). Square it (0.2869897957) and add it to both sides. Add '0.2869897957' to each side of the equation. 1.071428571y + 0.2869897957 + y2 = 0.2142857143 + 0.2869897957 Reorder the terms: 0.2869897957 + 1.071428571y + y2 = 0.2142857143 + 0.2869897957 Combine like terms: 0.2142857143 + 0.2869897957 = 0.50127551 0.2869897957 + 1.071428571y + y2 = 0.50127551 Factor a perfect square on the left side: (y + 0.5357142855)(y + 0.5357142855) = 0.50127551 Calculate the square root of the right side: 0.708008128 Break this problem into two subproblems by setting (y + 0.5357142855) equal to 0.708008128 and -0.708008128.Subproblem 1
y + 0.5357142855 = 0.708008128 Simplifying y + 0.5357142855 = 0.708008128 Reorder the terms: 0.5357142855 + y = 0.708008128 Solving 0.5357142855 + y = 0.708008128 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5357142855' to each side of the equation. 0.5357142855 + -0.5357142855 + y = 0.708008128 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + y = 0.708008128 + -0.5357142855 y = 0.708008128 + -0.5357142855 Combine like terms: 0.708008128 + -0.5357142855 = 0.1722938425 y = 0.1722938425 Simplifying y = 0.1722938425Subproblem 2
y + 0.5357142855 = -0.708008128 Simplifying y + 0.5357142855 = -0.708008128 Reorder the terms: 0.5357142855 + y = -0.708008128 Solving 0.5357142855 + y = -0.708008128 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5357142855' to each side of the equation. 0.5357142855 + -0.5357142855 + y = -0.708008128 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + y = -0.708008128 + -0.5357142855 y = -0.708008128 + -0.5357142855 Combine like terms: -0.708008128 + -0.5357142855 = -1.2437224135 y = -1.2437224135 Simplifying y = -1.2437224135Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.1722938425, -1.2437224135}
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