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Simplifying 25y2 + -35y + 9 = 0 Reorder the terms: 9 + -35y + 25y2 = 0 Solving 9 + -35y + 25y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.36 + -1.4y + y2 = 0 Move the constant term to the right: Add '-0.36' to each side of the equation. 0.36 + -1.4y + -0.36 + y2 = 0 + -0.36 Reorder the terms: 0.36 + -0.36 + -1.4y + y2 = 0 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 0.00 + -1.4y + y2 = 0 + -0.36 -1.4y + y2 = 0 + -0.36 Combine like terms: 0 + -0.36 = -0.36 -1.4y + y2 = -0.36 The y term is -1.4y. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4y + 0.49 + y2 = -0.36 + 0.49 Reorder the terms: 0.49 + -1.4y + y2 = -0.36 + 0.49 Combine like terms: -0.36 + 0.49 = 0.13 0.49 + -1.4y + y2 = 0.13 Factor a perfect square on the left side: (y + -0.7)(y + -0.7) = 0.13 Calculate the square root of the right side: 0.360555128 Break this problem into two subproblems by setting (y + -0.7) equal to 0.360555128 and -0.360555128.Subproblem 1
y + -0.7 = 0.360555128 Simplifying y + -0.7 = 0.360555128 Reorder the terms: -0.7 + y = 0.360555128 Solving -0.7 + y = 0.360555128 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + y = 0.360555128 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + y = 0.360555128 + 0.7 y = 0.360555128 + 0.7 Combine like terms: 0.360555128 + 0.7 = 1.060555128 y = 1.060555128 Simplifying y = 1.060555128Subproblem 2
y + -0.7 = -0.360555128 Simplifying y + -0.7 = -0.360555128 Reorder the terms: -0.7 + y = -0.360555128 Solving -0.7 + y = -0.360555128 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + y = -0.360555128 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + y = -0.360555128 + 0.7 y = -0.360555128 + 0.7 Combine like terms: -0.360555128 + 0.7 = 0.339444872 y = 0.339444872 Simplifying y = 0.339444872Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.060555128, 0.339444872}
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