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Simplifying 63 + -13y2 + 40y = 0 Reorder the terms: 63 + 40y + -13y2 = 0 Solving 63 + 40y + -13y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -4.846153846 + -3.076923077y + y2 = 0 Move the constant term to the right: Add '4.846153846' to each side of the equation. -4.846153846 + -3.076923077y + 4.846153846 + y2 = 0 + 4.846153846 Reorder the terms: -4.846153846 + 4.846153846 + -3.076923077y + y2 = 0 + 4.846153846 Combine like terms: -4.846153846 + 4.846153846 = 0.000000000 0.000000000 + -3.076923077y + y2 = 0 + 4.846153846 -3.076923077y + y2 = 0 + 4.846153846 Combine like terms: 0 + 4.846153846 = 4.846153846 -3.076923077y + y2 = 4.846153846 The y term is -3.076923077y. Take half its coefficient (-1.538461539). Square it (2.366863907) and add it to both sides. Add '2.366863907' to each side of the equation. -3.076923077y + 2.366863907 + y2 = 4.846153846 + 2.366863907 Reorder the terms: 2.366863907 + -3.076923077y + y2 = 4.846153846 + 2.366863907 Combine like terms: 4.846153846 + 2.366863907 = 7.213017753 2.366863907 + -3.076923077y + y2 = 7.213017753 Factor a perfect square on the left side: (y + -1.538461539)(y + -1.538461539) = 7.213017753 Calculate the square root of the right side: 2.685706193 Break this problem into two subproblems by setting (y + -1.538461539) equal to 2.685706193 and -2.685706193.Subproblem 1
y + -1.538461539 = 2.685706193 Simplifying y + -1.538461539 = 2.685706193 Reorder the terms: -1.538461539 + y = 2.685706193 Solving -1.538461539 + y = 2.685706193 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.538461539' to each side of the equation. -1.538461539 + 1.538461539 + y = 2.685706193 + 1.538461539 Combine like terms: -1.538461539 + 1.538461539 = 0.000000000 0.000000000 + y = 2.685706193 + 1.538461539 y = 2.685706193 + 1.538461539 Combine like terms: 2.685706193 + 1.538461539 = 4.224167732 y = 4.224167732 Simplifying y = 4.224167732Subproblem 2
y + -1.538461539 = -2.685706193 Simplifying y + -1.538461539 = -2.685706193 Reorder the terms: -1.538461539 + y = -2.685706193 Solving -1.538461539 + y = -2.685706193 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.538461539' to each side of the equation. -1.538461539 + 1.538461539 + y = -2.685706193 + 1.538461539 Combine like terms: -1.538461539 + 1.538461539 = 0.000000000 0.000000000 + y = -2.685706193 + 1.538461539 y = -2.685706193 + 1.538461539 Combine like terms: -2.685706193 + 1.538461539 = -1.147244654 y = -1.147244654 Simplifying y = -1.147244654Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.224167732, -1.147244654}
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