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Simplifying 16y2 + -112y + 14 = 0 Reorder the terms: 14 + -112y + 16y2 = 0 Solving 14 + -112y + 16y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -56y + 8y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -56y + 8y2)' equal to zero and attempt to solve: Simplifying 7 + -56y + 8y2 = 0 Solving 7 + -56y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.875 + -7y + y2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -7y + -0.875 + y2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -7y + y2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -7y + y2 = 0 + -0.875 -7y + y2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -7y + y2 = -0.875 The y term is -7y. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y + 12.25 + y2 = -0.875 + 12.25 Reorder the terms: 12.25 + -7y + y2 = -0.875 + 12.25 Combine like terms: -0.875 + 12.25 = 11.375 12.25 + -7y + y2 = 11.375 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 11.375 Calculate the square root of the right side: 3.372684391 Break this problem into two subproblems by setting (y + -3.5) equal to 3.372684391 and -3.372684391.Subproblem 1
y + -3.5 = 3.372684391 Simplifying y + -3.5 = 3.372684391 Reorder the terms: -3.5 + y = 3.372684391 Solving -3.5 + y = 3.372684391 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 3.372684391 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 3.372684391 + 3.5 y = 3.372684391 + 3.5 Combine like terms: 3.372684391 + 3.5 = 6.872684391 y = 6.872684391 Simplifying y = 6.872684391Subproblem 2
y + -3.5 = -3.372684391 Simplifying y + -3.5 = -3.372684391 Reorder the terms: -3.5 + y = -3.372684391 Solving -3.5 + y = -3.372684391 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = -3.372684391 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -3.372684391 + 3.5 y = -3.372684391 + 3.5 Combine like terms: -3.372684391 + 3.5 = 0.127315609 y = 0.127315609 Simplifying y = 0.127315609Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.872684391, 0.127315609}Solution
y = {6.872684391, 0.127315609}
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