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Simplifying 4y2 + -12y = -7 Reorder the terms: -12y + 4y2 = -7 Solving -12y + 4y2 = -7 Solving for variable 'y'. Reorder the terms: 7 + -12y + 4y2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + -12y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -3y + y2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -3y + -1.75 + y2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -3y + y2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -3y + y2 = 0 + -1.75 -3y + y2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -3y + y2 = -1.75 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = -1.75 + 2.25 Reorder the terms: 2.25 + -3y + y2 = -1.75 + 2.25 Combine like terms: -1.75 + 2.25 = 0.5 2.25 + -3y + y2 = 0.5 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (y + -1.5) equal to 0.707106781 and -0.707106781.Subproblem 1
y + -1.5 = 0.707106781 Simplifying y + -1.5 = 0.707106781 Reorder the terms: -1.5 + y = 0.707106781 Solving -1.5 + y = 0.707106781 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 0.707106781 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 0.707106781 + 1.5 y = 0.707106781 + 1.5 Combine like terms: 0.707106781 + 1.5 = 2.207106781 y = 2.207106781 Simplifying y = 2.207106781Subproblem 2
y + -1.5 = -0.707106781 Simplifying y + -1.5 = -0.707106781 Reorder the terms: -1.5 + y = -0.707106781 Solving -1.5 + y = -0.707106781 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -0.707106781 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -0.707106781 + 1.5 y = -0.707106781 + 1.5 Combine like terms: -0.707106781 + 1.5 = 0.792893219 y = 0.792893219 Simplifying y = 0.792893219Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.207106781, 0.792893219}
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