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Simplifying 10y2 + -30y + -2 = 0 Reorder the terms: -2 + -30y + 10y2 = 0 Solving -2 + -30y + 10y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -15y + 5y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -15y + 5y2)' equal to zero and attempt to solve: Simplifying -1 + -15y + 5y2 = 0 Solving -1 + -15y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -3y + y2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -3y + 0.2 + y2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -3y + y2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -3y + y2 = 0 + 0.2 -3y + y2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -3y + y2 = 0.2 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 0.2 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 0.2 + 2.25 Combine like terms: 0.2 + 2.25 = 2.45 2.25 + -3y + y2 = 2.45 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 2.45 Calculate the square root of the right side: 1.565247584 Break this problem into two subproblems by setting (y + -1.5) equal to 1.565247584 and -1.565247584.Subproblem 1
y + -1.5 = 1.565247584 Simplifying y + -1.5 = 1.565247584 Reorder the terms: -1.5 + y = 1.565247584 Solving -1.5 + y = 1.565247584 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 1.565247584 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 1.565247584 + 1.5 y = 1.565247584 + 1.5 Combine like terms: 1.565247584 + 1.5 = 3.065247584 y = 3.065247584 Simplifying y = 3.065247584Subproblem 2
y + -1.5 = -1.565247584 Simplifying y + -1.5 = -1.565247584 Reorder the terms: -1.5 + y = -1.565247584 Solving -1.5 + y = -1.565247584 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -1.565247584 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -1.565247584 + 1.5 y = -1.565247584 + 1.5 Combine like terms: -1.565247584 + 1.5 = -0.065247584 y = -0.065247584 Simplifying y = -0.065247584Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.065247584, -0.065247584}Solution
y = {3.065247584, -0.065247584}
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