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Simplifying 1.8y2 + 11y + -90 = 0 Reorder the terms: -90 + 11y + 1.8y2 = 0 Solving -90 + 11y + 1.8y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 1.8 the coefficient of the squared term: Divide each side by '1.8'. -50 + 6.111111111y + y2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 6.111111111y + 50 + y2 = 0 + 50 Reorder the terms: -50 + 50 + 6.111111111y + y2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 6.111111111y + y2 = 0 + 50 6.111111111y + y2 = 0 + 50 Combine like terms: 0 + 50 = 50 6.111111111y + y2 = 50 The y term is 6.111111111y. Take half its coefficient (3.055555556). Square it (9.336419756) and add it to both sides. Add '9.336419756' to each side of the equation. 6.111111111y + 9.336419756 + y2 = 50 + 9.336419756 Reorder the terms: 9.336419756 + 6.111111111y + y2 = 50 + 9.336419756 Combine like terms: 50 + 9.336419756 = 59.336419756 9.336419756 + 6.111111111y + y2 = 59.336419756 Factor a perfect square on the left side: (y + 3.055555556)(y + 3.055555556) = 59.336419756 Calculate the square root of the right side: 7.70301368 Break this problem into two subproblems by setting (y + 3.055555556) equal to 7.70301368 and -7.70301368.Subproblem 1
y + 3.055555556 = 7.70301368 Simplifying y + 3.055555556 = 7.70301368 Reorder the terms: 3.055555556 + y = 7.70301368 Solving 3.055555556 + y = 7.70301368 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.055555556' to each side of the equation. 3.055555556 + -3.055555556 + y = 7.70301368 + -3.055555556 Combine like terms: 3.055555556 + -3.055555556 = 0.000000000 0.000000000 + y = 7.70301368 + -3.055555556 y = 7.70301368 + -3.055555556 Combine like terms: 7.70301368 + -3.055555556 = 4.647458124 y = 4.647458124 Simplifying y = 4.647458124Subproblem 2
y + 3.055555556 = -7.70301368 Simplifying y + 3.055555556 = -7.70301368 Reorder the terms: 3.055555556 + y = -7.70301368 Solving 3.055555556 + y = -7.70301368 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.055555556' to each side of the equation. 3.055555556 + -3.055555556 + y = -7.70301368 + -3.055555556 Combine like terms: 3.055555556 + -3.055555556 = 0.000000000 0.000000000 + y = -7.70301368 + -3.055555556 y = -7.70301368 + -3.055555556 Combine like terms: -7.70301368 + -3.055555556 = -10.758569236 y = -10.758569236 Simplifying y = -10.758569236Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.647458124, -10.758569236}
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