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Simplifying 20y2 + -20y + -30 = 0 Reorder the terms: -30 + -20y + 20y2 = 0 Solving -30 + -20y + 20y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '10'. 10(-3 + -2y + 2y2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-3 + -2y + 2y2)' equal to zero and attempt to solve: Simplifying -3 + -2y + 2y2 = 0 Solving -3 + -2y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -1y + y2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1y + 1.5 + y2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1y + y2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1y + y2 = 0 + 1.5 -1y + y2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1y + y2 = 1.5 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 1.5 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 1.5 + 0.25 Combine like terms: 1.5 + 0.25 = 1.75 0.25 + -1y + y2 = 1.75 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (y + -0.5) equal to 1.322875656 and -1.322875656.Subproblem 1
y + -0.5 = 1.322875656 Simplifying y + -0.5 = 1.322875656 Reorder the terms: -0.5 + y = 1.322875656 Solving -0.5 + y = 1.322875656 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 1.322875656 + 0.5 y = 1.322875656 + 0.5 Combine like terms: 1.322875656 + 0.5 = 1.822875656 y = 1.822875656 Simplifying y = 1.822875656Subproblem 2
y + -0.5 = -1.322875656 Simplifying y + -0.5 = -1.322875656 Reorder the terms: -0.5 + y = -1.322875656 Solving -0.5 + y = -1.322875656 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -1.322875656 + 0.5 y = -1.322875656 + 0.5 Combine like terms: -1.322875656 + 0.5 = -0.822875656 y = -0.822875656 Simplifying y = -0.822875656Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.822875656, -0.822875656}Solution
y = {1.822875656, -0.822875656}
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