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Simplifying 4y2 + -24y + 29 = 0 Reorder the terms: 29 + -24y + 4y2 = 0 Solving 29 + -24y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7.25 + -6y + y2 = 0 Move the constant term to the right: Add '-7.25' to each side of the equation. 7.25 + -6y + -7.25 + y2 = 0 + -7.25 Reorder the terms: 7.25 + -7.25 + -6y + y2 = 0 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + -6y + y2 = 0 + -7.25 -6y + y2 = 0 + -7.25 Combine like terms: 0 + -7.25 = -7.25 -6y + y2 = -7.25 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = -7.25 + 9 Reorder the terms: 9 + -6y + y2 = -7.25 + 9 Combine like terms: -7.25 + 9 = 1.75 9 + -6y + y2 = 1.75 Factor a perfect square on the left side: (y + -3)(y + -3) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (y + -3) equal to 1.322875656 and -1.322875656.Subproblem 1
y + -3 = 1.322875656 Simplifying y + -3 = 1.322875656 Reorder the terms: -3 + y = 1.322875656 Solving -3 + y = 1.322875656 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 1.322875656 + 3 Combine like terms: -3 + 3 = 0 0 + y = 1.322875656 + 3 y = 1.322875656 + 3 Combine like terms: 1.322875656 + 3 = 4.322875656 y = 4.322875656 Simplifying y = 4.322875656Subproblem 2
y + -3 = -1.322875656 Simplifying y + -3 = -1.322875656 Reorder the terms: -3 + y = -1.322875656 Solving -3 + y = -1.322875656 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -1.322875656 + 3 Combine like terms: -3 + 3 = 0 0 + y = -1.322875656 + 3 y = -1.322875656 + 3 Combine like terms: -1.322875656 + 3 = 1.677124344 y = 1.677124344 Simplifying y = 1.677124344Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.322875656, 1.677124344}
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