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Simplifying 4y + -1y * y = -1000 Multiply y * y 4y + -1y2 = -1000 Solving 4y + -1y2 = -1000 Solving for variable 'y'. Reorder the terms: 1000 + 4y + -1y2 = -1000 + 1000 Combine like terms: -1000 + 1000 = 0 1000 + 4y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1000 + -4y + y2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -4y + 1000 + y2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -4y + y2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -4y + y2 = 0 + 1000 -4y + y2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -4y + y2 = 1000 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 1000 + 4 Reorder the terms: 4 + -4y + y2 = 1000 + 4 Combine like terms: 1000 + 4 = 1004 4 + -4y + y2 = 1004 Factor a perfect square on the left side: (y + -2)(y + -2) = 1004 Calculate the square root of the right side: 31.685959036 Break this problem into two subproblems by setting (y + -2) equal to 31.685959036 and -31.685959036.Subproblem 1
y + -2 = 31.685959036 Simplifying y + -2 = 31.685959036 Reorder the terms: -2 + y = 31.685959036 Solving -2 + y = 31.685959036 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 31.685959036 + 2 Combine like terms: -2 + 2 = 0 0 + y = 31.685959036 + 2 y = 31.685959036 + 2 Combine like terms: 31.685959036 + 2 = 33.685959036 y = 33.685959036 Simplifying y = 33.685959036Subproblem 2
y + -2 = -31.685959036 Simplifying y + -2 = -31.685959036 Reorder the terms: -2 + y = -31.685959036 Solving -2 + y = -31.685959036 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -31.685959036 + 2 Combine like terms: -2 + 2 = 0 0 + y = -31.685959036 + 2 y = -31.685959036 + 2 Combine like terms: -31.685959036 + 2 = -29.685959036 y = -29.685959036 Simplifying y = -29.685959036Solution
The solution to the problem is based on the solutions from the subproblems. y = {33.685959036, -29.685959036}
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