(y-4)(y-4)=49

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Solution for (y-4)(y-4)=49 equation:


Simplifying
(y + -4)(y + -4) = 49

Reorder the terms:
(-4 + y)(y + -4) = 49

Reorder the terms:
(-4 + y)(-4 + y) = 49

Multiply (-4 + y) * (-4 + y)
(-4(-4 + y) + y(-4 + y)) = 49
((-4 * -4 + y * -4) + y(-4 + y)) = 49
((16 + -4y) + y(-4 + y)) = 49
(16 + -4y + (-4 * y + y * y)) = 49
(16 + -4y + (-4y + y2)) = 49

Combine like terms: -4y + -4y = -8y
(16 + -8y + y2) = 49

Solving
16 + -8y + y2 = 49

Solving for variable 'y'.

Reorder the terms:
16 + -49 + -8y + y2 = 49 + -49

Combine like terms: 16 + -49 = -33
-33 + -8y + y2 = 49 + -49

Combine like terms: 49 + -49 = 0
-33 + -8y + y2 = 0

Factor a trinomial.
(-3 + -1y)(11 + -1y) = 0

Subproblem 1

Set the factor '(-3 + -1y)' equal to zero and attempt to solve: Simplifying -3 + -1y = 0 Solving -3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1y = 0 + 3 -1y = 0 + 3 Combine like terms: 0 + 3 = 3 -1y = 3 Divide each side by '-1'. y = -3 Simplifying y = -3

Subproblem 2

Set the factor '(11 + -1y)' equal to zero and attempt to solve: Simplifying 11 + -1y = 0 Solving 11 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1y = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1y = 0 + -11 -1y = 0 + -11 Combine like terms: 0 + -11 = -11 -1y = -11 Divide each side by '-1'. y = 11 Simplifying y = 11

Solution

y = {-3, 11}

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