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Simplifying 7y2 + -3y + -2 = -5y Reorder the terms: -2 + -3y + 7y2 = -5y Solving -2 + -3y + 7y2 = -5y Solving for variable 'y'. Reorder the terms: -2 + -3y + 5y + 7y2 = -5y + 5y Combine like terms: -3y + 5y = 2y -2 + 2y + 7y2 = -5y + 5y Combine like terms: -5y + 5y = 0 -2 + 2y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 0.2857142857y + y2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857y + 0.2857142857 + y2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 0.2857142857y + y2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 0.2857142857y + y2 = 0 + 0.2857142857 0.2857142857y + y2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 0.2857142857y + y2 = 0.2857142857 The y term is 0.2857142857y. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857y + 0.02040816328 + y2 = 0.2857142857 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857y + y2 = 0.2857142857 + 0.02040816328 Combine like terms: 0.2857142857 + 0.02040816328 = 0.30612244898 0.02040816328 + 0.2857142857y + y2 = 0.30612244898 Factor a perfect square on the left side: (y + 0.1428571429)(y + 0.1428571429) = 0.30612244898 Calculate the square root of the right side: 0.553283335 Break this problem into two subproblems by setting (y + 0.1428571429) equal to 0.553283335 and -0.553283335.Subproblem 1
y + 0.1428571429 = 0.553283335 Simplifying y + 0.1428571429 = 0.553283335 Reorder the terms: 0.1428571429 + y = 0.553283335 Solving 0.1428571429 + y = 0.553283335 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + y = 0.553283335 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + y = 0.553283335 + -0.1428571429 y = 0.553283335 + -0.1428571429 Combine like terms: 0.553283335 + -0.1428571429 = 0.4104261921 y = 0.4104261921 Simplifying y = 0.4104261921Subproblem 2
y + 0.1428571429 = -0.553283335 Simplifying y + 0.1428571429 = -0.553283335 Reorder the terms: 0.1428571429 + y = -0.553283335 Solving 0.1428571429 + y = -0.553283335 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + y = -0.553283335 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + y = -0.553283335 + -0.1428571429 y = -0.553283335 + -0.1428571429 Combine like terms: -0.553283335 + -0.1428571429 = -0.6961404779 y = -0.6961404779 Simplifying y = -0.6961404779Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.4104261921, -0.6961404779}
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