What are the solutions to the equation 28.18^2=w^2+(4w)^2 ?

The solutions to the equation 28.18^2=w^2+(4w)^2 are w=-6.83465…,w=6.83465…

Find the zeros of 28.18^2=w^2+(4w)^2

The zeros of 28.18^2=w^2+(4w)^2 are w=-6.83465…,w=6.83465…

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28.1 8^{2} = w^{2} + (4 w)^{2}

w = - 6.83465 \dots, w = 6.83465 \dots

Solution steps

28.1 8^{2} = w^{2} + (4 w)^{2}

Expand

28.1 8^{2} : 794.1124

Expand

w^{2} + (4 w)^{2} : 17 w^{2}

794.1124 = 17 w^{2}

Switch sides

17 w^{2} = 794.1124

Move

794.1124

to the left side

17 w^{2} - 794.1124 = 0

Factor

17 w^{2} - 794.1124 : (4.12310 \dots w + 28.18) (4.12310 \dots w - 28.18)

(4.12310 \dots w + 28.18) (4.12310 \dots w - 28.18) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

4.12310 \dots w + 28.18 = 0 or 4.12310 \dots w - 28.18 = 0

Solve

4.12310 \dots w + 28.18 = 0 : w = - 6.83465 \dots

Solve

4.12310 \dots w - 28.18 = 0 : w = 6.83465 \dots

The solutions to the quadratic equation are:

w = - 6.83465 \dots, w = 6.83465 \dots

z^{2} = - 16

(26 - x)^{2} + (13 - x)^{2} = x^{2}

2 (x + 3)^{2} = 0

(x + 2) (3 x - 1) = (x - 5)^{2}

(4 + 3 x)^{2} + x^{2} = 146

What are the solutions to the equation 28.18^2=w^2+(4w)^2 ?
The solutions to the equation 28.18^2=w^2+(4w)^2 are w=-6.83465…,w=6.83465…
Find the zeros of 28.18^2=w^2+(4w)^2
The zeros of 28.18^2=w^2+(4w)^2 are w=-6.83465…,w=6.83465…