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Simplifying 7y2 + -7y + -12 = 0 Reorder the terms: -12 + -7y + 7y2 = 0 Solving -12 + -7y + 7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.714285714 + -1y + y2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + -1y + 1.714285714 + y2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + -1y + y2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + -1y + y2 = 0 + 1.714285714 -1y + y2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 -1y + y2 = 1.714285714 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 = 1.714285714 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 1.714285714 + 0.25 Combine like terms: 1.714285714 + 0.25 = 1.964285714 0.25 + -1y + y2 = 1.964285714 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 1.964285714 Calculate the square root of the right side: 1.401529776 Break this problem into two subproblems by setting (y + -0.5) equal to 1.401529776 and -1.401529776.Subproblem 1
y + -0.5 = 1.401529776 Simplifying y + -0.5 = 1.401529776 Reorder the terms: -0.5 + y = 1.401529776 Solving -0.5 + y = 1.401529776 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 = 1.401529776 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 1.401529776 + 0.5 y = 1.401529776 + 0.5 Combine like terms: 1.401529776 + 0.5 = 1.901529776 y = 1.901529776 Simplifying y = 1.901529776Subproblem 2
y + -0.5 = -1.401529776 Simplifying y + -0.5 = -1.401529776 Reorder the terms: -0.5 + y = -1.401529776 Solving -0.5 + y = -1.401529776 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 = -1.401529776 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -1.401529776 + 0.5 y = -1.401529776 + 0.5 Combine like terms: -1.401529776 + 0.5 = -0.901529776 y = -0.901529776 Simplifying y = -0.901529776Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.901529776, -0.901529776}
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