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Simplifying 5y2 + 12y + -7 = 0 Reorder the terms: -7 + 12y + 5y2 = 0 Solving -7 + 12y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 2.4y + y2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 2.4y + 1.4 + y2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 2.4y + y2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 2.4y + y2 = 0 + 1.4 2.4y + y2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 2.4y + y2 = 1.4 The y term is 2.4y. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4y + 1.44 + y2 = 1.4 + 1.44 Reorder the terms: 1.44 + 2.4y + y2 = 1.4 + 1.44 Combine like terms: 1.4 + 1.44 = 2.84 1.44 + 2.4y + y2 = 2.84 Factor a perfect square on the left side: (y + 1.2)(y + 1.2) = 2.84 Calculate the square root of the right side: 1.685229955 Break this problem into two subproblems by setting (y + 1.2) equal to 1.685229955 and -1.685229955.Subproblem 1
y + 1.2 = 1.685229955 Simplifying y + 1.2 = 1.685229955 Reorder the terms: 1.2 + y = 1.685229955 Solving 1.2 + y = 1.685229955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + y = 1.685229955 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + y = 1.685229955 + -1.2 y = 1.685229955 + -1.2 Combine like terms: 1.685229955 + -1.2 = 0.485229955 y = 0.485229955 Simplifying y = 0.485229955Subproblem 2
y + 1.2 = -1.685229955 Simplifying y + 1.2 = -1.685229955 Reorder the terms: 1.2 + y = -1.685229955 Solving 1.2 + y = -1.685229955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + y = -1.685229955 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + y = -1.685229955 + -1.2 y = -1.685229955 + -1.2 Combine like terms: -1.685229955 + -1.2 = -2.885229955 y = -2.885229955 Simplifying y = -2.885229955Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.485229955, -2.885229955}
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