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Simplifying 6 + -1y * 5y + -6y = 0 Reorder the terms for easier multiplication: 6 + -1 * 5y * y + -6y = 0 Multiply -1 * 5 6 + -5y * y + -6y = 0 Multiply y * y 6 + -5y2 + -6y = 0 Reorder the terms: 6 + -6y + -5y2 = 0 Solving 6 + -6y + -5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.2 + 1.2y + y2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 1.2y + 1.2 + y2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 1.2y + y2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 1.2y + y2 = 0 + 1.2 1.2y + y2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 1.2y + y2 = 1.2 The y term is 1.2y. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2y + 0.36 + y2 = 1.2 + 0.36 Reorder the terms: 0.36 + 1.2y + y2 = 1.2 + 0.36 Combine like terms: 1.2 + 0.36 = 1.56 0.36 + 1.2y + y2 = 1.56 Factor a perfect square on the left side: (y + 0.6)(y + 0.6) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (y + 0.6) equal to 1.2489996 and -1.2489996.Subproblem 1
y + 0.6 = 1.2489996 Simplifying y + 0.6 = 1.2489996 Reorder the terms: 0.6 + y = 1.2489996 Solving 0.6 + y = 1.2489996 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + y = 1.2489996 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + y = 1.2489996 + -0.6 y = 1.2489996 + -0.6 Combine like terms: 1.2489996 + -0.6 = 0.6489996 y = 0.6489996 Simplifying y = 0.6489996Subproblem 2
y + 0.6 = -1.2489996 Simplifying y + 0.6 = -1.2489996 Reorder the terms: 0.6 + y = -1.2489996 Solving 0.6 + y = -1.2489996 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + y = -1.2489996 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + y = -1.2489996 + -0.6 y = -1.2489996 + -0.6 Combine like terms: -1.2489996 + -0.6 = -1.8489996 y = -1.8489996 Simplifying y = -1.8489996Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.6489996, -1.8489996}
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