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Simplifying 2y + -5 = 1y(1y) + -62 Reorder the terms: -5 + 2y = 1y(1y) + -62 Remove parenthesis around (1y) -5 + 2y = 1y * 1y + -62 Reorder the terms for easier multiplication: -5 + 2y = 1 * 1y * y + -62 Multiply 1 * 1 -5 + 2y = 1y * y + -62 Multiply y * y -5 + 2y = 1y2 + -62 Reorder the terms: -5 + 2y = -62 + 1y2 Solving -5 + 2y = -62 + 1y2 Solving for variable 'y'. Reorder the terms: -5 + 62 + 2y + -1y2 = -62 + 1y2 + 62 + -1y2 Combine like terms: -5 + 62 = 57 57 + 2y + -1y2 = -62 + 1y2 + 62 + -1y2 Reorder the terms: 57 + 2y + -1y2 = -62 + 62 + 1y2 + -1y2 Combine like terms: -62 + 62 = 0 57 + 2y + -1y2 = 0 + 1y2 + -1y2 57 + 2y + -1y2 = 1y2 + -1y2 Combine like terms: 1y2 + -1y2 = 0 57 + 2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -57 + -2y + y2 = 0 Move the constant term to the right: Add '57' to each side of the equation. -57 + -2y + 57 + y2 = 0 + 57 Reorder the terms: -57 + 57 + -2y + y2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + -2y + y2 = 0 + 57 -2y + y2 = 0 + 57 Combine like terms: 0 + 57 = 57 -2y + y2 = 57 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 57 + 1 Reorder the terms: 1 + -2y + y2 = 57 + 1 Combine like terms: 57 + 1 = 58 1 + -2y + y2 = 58 Factor a perfect square on the left side: (y + -1)(y + -1) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (y + -1) equal to 7.615773106 and -7.615773106.Subproblem 1
y + -1 = 7.615773106 Simplifying y + -1 = 7.615773106 Reorder the terms: -1 + y = 7.615773106 Solving -1 + y = 7.615773106 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 7.615773106 + 1 Combine like terms: -1 + 1 = 0 0 + y = 7.615773106 + 1 y = 7.615773106 + 1 Combine like terms: 7.615773106 + 1 = 8.615773106 y = 8.615773106 Simplifying y = 8.615773106Subproblem 2
y + -1 = -7.615773106 Simplifying y + -1 = -7.615773106 Reorder the terms: -1 + y = -7.615773106 Solving -1 + y = -7.615773106 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -7.615773106 + 1 Combine like terms: -1 + 1 = 0 0 + y = -7.615773106 + 1 y = -7.615773106 + 1 Combine like terms: -7.615773106 + 1 = -6.615773106 y = -6.615773106 Simplifying y = -6.615773106Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.615773106, -6.615773106}
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