Solved on Jan 19, 2024

Solve vw2+y=xvw^2 + y = x for ww. Given v=5,x=38,y=7v=5, x=38, y=-7, find ww.

STEP 1

Assumptions
1. The equation to solve is vw2+y=x v w^{2} + y = x .
2. The given values are v=5 v = 5 , x=38 x = 38 , and y=7 y = -7 .
3. We need to solve for w w .

STEP 2

Isolate the term containing w w on one side of the equation.
vw2=xy v w^{2} = x - y

STEP 3

Substitute the given values for v v , x x , and y y into the equation.
5w2=38(7) 5 w^{2} = 38 - (-7)

STEP 4

Calculate the right side of the equation.
5w2=38+7 5 w^{2} = 38 + 7

STEP 5

Add the numbers to find the value.
5w2=45 5 w^{2} = 45

STEP 6

Divide both sides of the equation by 5 to solve for w2 w^{2} .
w2=455 w^{2} = \frac{45}{5}

STEP 7

Calculate the division to find w2 w^{2} .
w2=9 w^{2} = 9

STEP 8

Take the square root of both sides to solve for w w . Remember that taking the square root can result in both a positive and negative solution.
w=±9 w = \pm\sqrt{9}

STEP 9

Calculate the square root of 9.
w=±3 w = \pm 3
So, the solutions for w w are w=3 w = 3 and w=3 w = -3 .

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