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Simplifying 5y + -13y2 + 7 = 0 Reorder the terms: 7 + 5y + -13y2 = 0 Solving 7 + 5y + -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'. -0.5384615385 + -0.3846153846y + y2 = 0 Move the constant term to the right: Add '0.5384615385' to each side of the equation. -0.5384615385 + -0.3846153846y + 0.5384615385 + y2 = 0 + 0.5384615385 Reorder the terms: -0.5384615385 + 0.5384615385 + -0.3846153846y + y2 = 0 + 0.5384615385 Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000 0.0000000000 + -0.3846153846y + y2 = 0 + 0.5384615385 -0.3846153846y + y2 = 0 + 0.5384615385 Combine like terms: 0 + 0.5384615385 = 0.5384615385 -0.3846153846y + y2 = 0.5384615385 The y term is -0.3846153846y. Take half its coefficient (-0.1923076923). Square it (0.03698224852) and add it to both sides. Add '0.03698224852' to each side of the equation. -0.3846153846y + 0.03698224852 + y2 = 0.5384615385 + 0.03698224852 Reorder the terms: 0.03698224852 + -0.3846153846y + y2 = 0.5384615385 + 0.03698224852 Combine like terms: 0.5384615385 + 0.03698224852 = 0.57544378702 0.03698224852 + -0.3846153846y + y2 = 0.57544378702 Factor a perfect square on the left side: (y + -0.1923076923)(y + -0.1923076923) = 0.57544378702 Calculate the square root of the right side: 0.758580112 Break this problem into two subproblems by setting (y + -0.1923076923) equal to 0.758580112 and -0.758580112.Subproblem 1
y + -0.1923076923 = 0.758580112 Simplifying y + -0.1923076923 = 0.758580112 Reorder the terms: -0.1923076923 + y = 0.758580112 Solving -0.1923076923 + y = 0.758580112 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1923076923' to each side of the equation. -0.1923076923 + 0.1923076923 + y = 0.758580112 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + y = 0.758580112 + 0.1923076923 y = 0.758580112 + 0.1923076923 Combine like terms: 0.758580112 + 0.1923076923 = 0.9508878043 y = 0.9508878043 Simplifying y = 0.9508878043Subproblem 2
y + -0.1923076923 = -0.758580112 Simplifying y + -0.1923076923 = -0.758580112 Reorder the terms: -0.1923076923 + y = -0.758580112 Solving -0.1923076923 + y = -0.758580112 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1923076923' to each side of the equation. -0.1923076923 + 0.1923076923 + y = -0.758580112 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + y = -0.758580112 + 0.1923076923 y = -0.758580112 + 0.1923076923 Combine like terms: -0.758580112 + 0.1923076923 = -0.5662724197 y = -0.5662724197 Simplifying y = -0.5662724197Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.9508878043, -0.5662724197}
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