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Simplifying -10y2 + -3y + 3 = 0 Reorder the terms: 3 + -3y + -10y2 = 0 Solving 3 + -3y + -10y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.3 + 0.3y + y2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.3y + 0.3 + y2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.3y + y2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.3y + y2 = 0 + 0.3 0.3y + y2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 0.3y + y2 = 0.3 The y term is 0.3y. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3y + 0.0225 + y2 = 0.3 + 0.0225 Reorder the terms: 0.0225 + 0.3y + y2 = 0.3 + 0.0225 Combine like terms: 0.3 + 0.0225 = 0.3225 0.0225 + 0.3y + y2 = 0.3225 Factor a perfect square on the left side: (y + 0.15)(y + 0.15) = 0.3225 Calculate the square root of the right side: 0.567890835 Break this problem into two subproblems by setting (y + 0.15) equal to 0.567890835 and -0.567890835.Subproblem 1
y + 0.15 = 0.567890835 Simplifying y + 0.15 = 0.567890835 Reorder the terms: 0.15 + y = 0.567890835 Solving 0.15 + y = 0.567890835 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + y = 0.567890835 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + y = 0.567890835 + -0.15 y = 0.567890835 + -0.15 Combine like terms: 0.567890835 + -0.15 = 0.417890835 y = 0.417890835 Simplifying y = 0.417890835Subproblem 2
y + 0.15 = -0.567890835 Simplifying y + 0.15 = -0.567890835 Reorder the terms: 0.15 + y = -0.567890835 Solving 0.15 + y = -0.567890835 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + y = -0.567890835 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + y = -0.567890835 + -0.15 y = -0.567890835 + -0.15 Combine like terms: -0.567890835 + -0.15 = -0.717890835 y = -0.717890835 Simplifying y = -0.717890835Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.417890835, -0.717890835}
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