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Simplifying 35y2 + 14y + -4 = 0 Reorder the terms: -4 + 14y + 35y2 = 0 Solving -4 + 14y + 35y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.1142857143 + 0.4y + y2 = 0 Move the constant term to the right: Add '0.1142857143' to each side of the equation. -0.1142857143 + 0.4y + 0.1142857143 + y2 = 0 + 0.1142857143 Reorder the terms: -0.1142857143 + 0.1142857143 + 0.4y + y2 = 0 + 0.1142857143 Combine like terms: -0.1142857143 + 0.1142857143 = 0.0000000000 0.0000000000 + 0.4y + y2 = 0 + 0.1142857143 0.4y + y2 = 0 + 0.1142857143 Combine like terms: 0 + 0.1142857143 = 0.1142857143 0.4y + y2 = 0.1142857143 The y term is 0.4y. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4y + 0.04 + y2 = 0.1142857143 + 0.04 Reorder the terms: 0.04 + 0.4y + y2 = 0.1142857143 + 0.04 Combine like terms: 0.1142857143 + 0.04 = 0.1542857143 0.04 + 0.4y + y2 = 0.1542857143 Factor a perfect square on the left side: (y + 0.2)(y + 0.2) = 0.1542857143 Calculate the square root of the right side: 0.392792202 Break this problem into two subproblems by setting (y + 0.2) equal to 0.392792202 and -0.392792202.Subproblem 1
y + 0.2 = 0.392792202 Simplifying y + 0.2 = 0.392792202 Reorder the terms: 0.2 + y = 0.392792202 Solving 0.2 + y = 0.392792202 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y = 0.392792202 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = 0.392792202 + -0.2 y = 0.392792202 + -0.2 Combine like terms: 0.392792202 + -0.2 = 0.192792202 y = 0.192792202 Simplifying y = 0.192792202Subproblem 2
y + 0.2 = -0.392792202 Simplifying y + 0.2 = -0.392792202 Reorder the terms: 0.2 + y = -0.392792202 Solving 0.2 + y = -0.392792202 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y = -0.392792202 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = -0.392792202 + -0.2 y = -0.392792202 + -0.2 Combine like terms: -0.392792202 + -0.2 = -0.592792202 y = -0.592792202 Simplifying y = -0.592792202Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.192792202, -0.592792202}
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