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Simplifying y * y = -2(2y + -35) Multiply y * y y2 = -2(2y + -35) Reorder the terms: y2 = -2(-35 + 2y) y2 = (-35 * -2 + 2y * -2) y2 = (70 + -4y) Solving y2 = 70 + -4y Solving for variable 'y'. Reorder the terms: -70 + 4y + y2 = 70 + -4y + -70 + 4y Reorder the terms: -70 + 4y + y2 = 70 + -70 + -4y + 4y Combine like terms: 70 + -70 = 0 -70 + 4y + y2 = 0 + -4y + 4y -70 + 4y + y2 = -4y + 4y Combine like terms: -4y + 4y = 0 -70 + 4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + 4y + 70 + y2 = 0 + 70 Reorder the terms: -70 + 70 + 4y + y2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 4y + y2 = 0 + 70 4y + y2 = 0 + 70 Combine like terms: 0 + 70 = 70 4y + y2 = 70 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 = 70 + 4 Reorder the terms: 4 + 4y + y2 = 70 + 4 Combine like terms: 70 + 4 = 74 4 + 4y + y2 = 74 Factor a perfect square on the left side: (y + 2)(y + 2) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (y + 2) equal to 8.602325267 and -8.602325267.Subproblem 1
y + 2 = 8.602325267 Simplifying y + 2 = 8.602325267 Reorder the terms: 2 + y = 8.602325267 Solving 2 + y = 8.602325267 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 = 8.602325267 + -2 Combine like terms: 2 + -2 = 0 0 + y = 8.602325267 + -2 y = 8.602325267 + -2 Combine like terms: 8.602325267 + -2 = 6.602325267 y = 6.602325267 Simplifying y = 6.602325267Subproblem 2
y + 2 = -8.602325267 Simplifying y + 2 = -8.602325267 Reorder the terms: 2 + y = -8.602325267 Solving 2 + y = -8.602325267 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 = -8.602325267 + -2 Combine like terms: 2 + -2 = 0 0 + y = -8.602325267 + -2 y = -8.602325267 + -2 Combine like terms: -8.602325267 + -2 = -10.602325267 y = -10.602325267 Simplifying y = -10.602325267Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.602325267, -10.602325267}
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