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Simplifying 6y + -4y2 = -7 Solving 6y + -4y2 = -7 Solving for variable 'y'. Reorder the terms: 7 + 6y + -4y2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 6y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.75 + -1.5y + y2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -1.5y + 1.75 + y2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -1.5y + y2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -1.5y + y2 = 0 + 1.75 -1.5y + y2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -1.5y + y2 = 1.75 The y term is -1.5y. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5y + 0.5625 + y2 = 1.75 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = 1.75 + 0.5625 Combine like terms: 1.75 + 0.5625 = 2.3125 0.5625 + -1.5y + y2 = 2.3125 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = 2.3125 Calculate the square root of the right side: 1.520690633 Break this problem into two subproblems by setting (y + -0.75) equal to 1.520690633 and -1.520690633.Subproblem 1
y + -0.75 = 1.520690633 Simplifying y + -0.75 = 1.520690633 Reorder the terms: -0.75 + y = 1.520690633 Solving -0.75 + y = 1.520690633 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = 1.520690633 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = 1.520690633 + 0.75 y = 1.520690633 + 0.75 Combine like terms: 1.520690633 + 0.75 = 2.270690633 y = 2.270690633 Simplifying y = 2.270690633Subproblem 2
y + -0.75 = -1.520690633 Simplifying y + -0.75 = -1.520690633 Reorder the terms: -0.75 + y = -1.520690633 Solving -0.75 + y = -1.520690633 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = -1.520690633 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = -1.520690633 + 0.75 y = -1.520690633 + 0.75 Combine like terms: -1.520690633 + 0.75 = -0.770690633 y = -0.770690633 Simplifying y = -0.770690633Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.270690633, -0.770690633}
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