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Simplifying 7y2 + 9y + -18 = 0 Reorder the terms: -18 + 9y + 7y2 = 0 Solving -18 + 9y + 7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.571428571 + 1.285714286y + y2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + 1.285714286y + 2.571428571 + y2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + 1.285714286y + y2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + 1.285714286y + y2 = 0 + 2.571428571 1.285714286y + y2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 1.285714286y + y2 = 2.571428571 The y term is 1.285714286y. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286y + 0.4132653063 + y2 = 2.571428571 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286y + y2 = 2.571428571 + 0.4132653063 Combine like terms: 2.571428571 + 0.4132653063 = 2.9846938773 0.4132653063 + 1.285714286y + y2 = 2.9846938773 Factor a perfect square on the left side: (y + 0.642857143)(y + 0.642857143) = 2.9846938773 Calculate the square root of the right side: 1.72762666 Break this problem into two subproblems by setting (y + 0.642857143) equal to 1.72762666 and -1.72762666.Subproblem 1
y + 0.642857143 = 1.72762666 Simplifying y + 0.642857143 = 1.72762666 Reorder the terms: 0.642857143 + y = 1.72762666 Solving 0.642857143 + y = 1.72762666 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + y = 1.72762666 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + y = 1.72762666 + -0.642857143 y = 1.72762666 + -0.642857143 Combine like terms: 1.72762666 + -0.642857143 = 1.084769517 y = 1.084769517 Simplifying y = 1.084769517Subproblem 2
y + 0.642857143 = -1.72762666 Simplifying y + 0.642857143 = -1.72762666 Reorder the terms: 0.642857143 + y = -1.72762666 Solving 0.642857143 + y = -1.72762666 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + y = -1.72762666 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + y = -1.72762666 + -0.642857143 y = -1.72762666 + -0.642857143 Combine like terms: -1.72762666 + -0.642857143 = -2.370483803 y = -2.370483803 Simplifying y = -2.370483803Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.084769517, -2.370483803}
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