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Simplifying 7y2 + 47y + -10 = 0 Reorder the terms: -10 + 47y + 7y2 = 0 Solving -10 + 47y + 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'. -1.428571429 + 6.714285714y + y2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 6.714285714y + 1.428571429 + y2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 6.714285714y + y2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 6.714285714y + y2 = 0 + 1.428571429 6.714285714y + y2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 6.714285714y + y2 = 1.428571429 The y term is 6.714285714y. Take half its coefficient (3.357142857). Square it (11.27040816) and add it to both sides. Add '11.27040816' to each side of the equation. 6.714285714y + 11.27040816 + y2 = 1.428571429 + 11.27040816 Reorder the terms: 11.27040816 + 6.714285714y + y2 = 1.428571429 + 11.27040816 Combine like terms: 1.428571429 + 11.27040816 = 12.698979589 11.27040816 + 6.714285714y + y2 = 12.698979589 Factor a perfect square on the left side: (y + 3.357142857)(y + 3.357142857) = 12.698979589 Calculate the square root of the right side: 3.563562766 Break this problem into two subproblems by setting (y + 3.357142857) equal to 3.563562766 and -3.563562766.Subproblem 1
y + 3.357142857 = 3.563562766 Simplifying y + 3.357142857 = 3.563562766 Reorder the terms: 3.357142857 + y = 3.563562766 Solving 3.357142857 + y = 3.563562766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.357142857' to each side of the equation. 3.357142857 + -3.357142857 + y = 3.563562766 + -3.357142857 Combine like terms: 3.357142857 + -3.357142857 = 0.000000000 0.000000000 + y = 3.563562766 + -3.357142857 y = 3.563562766 + -3.357142857 Combine like terms: 3.563562766 + -3.357142857 = 0.206419909 y = 0.206419909 Simplifying y = 0.206419909Subproblem 2
y + 3.357142857 = -3.563562766 Simplifying y + 3.357142857 = -3.563562766 Reorder the terms: 3.357142857 + y = -3.563562766 Solving 3.357142857 + y = -3.563562766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.357142857' to each side of the equation. 3.357142857 + -3.357142857 + y = -3.563562766 + -3.357142857 Combine like terms: 3.357142857 + -3.357142857 = 0.000000000 0.000000000 + y = -3.563562766 + -3.357142857 y = -3.563562766 + -3.357142857 Combine like terms: -3.563562766 + -3.357142857 = -6.920705623 y = -6.920705623 Simplifying y = -6.920705623Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.206419909, -6.920705623}
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