What are the solutions to the equation 29.12^2=w^2+(3w)^2 ?

The solutions to the equation 29.12^2=w^2+(3w)^2 are w=-9.20855…,w=9.20855…

Find the zeros of 29.12^2=w^2+(3w)^2

The zeros of 29.12^2=w^2+(3w)^2 are w=-9.20855…,w=9.20855…

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29.1 2^{2} = w^{2} + (3 w)^{2}

w = - 9.20855 \dots, w = 9.20855 \dots

Solution steps

29.1 2^{2} = w^{2} + (3 w)^{2}

Expand

29.1 2^{2} : 847.9744

Expand

w^{2} + (3 w)^{2} : 10 w^{2}

847.9744 = 10 w^{2}

Switch sides

10 w^{2} = 847.9744

Move

847.9744

to the left side

10 w^{2} - 847.9744 = 0

Factor

10 w^{2} - 847.9744 : (3.16227 \dots w + 29.12) (3.16227 \dots w - 29.12)

(3.16227 \dots w + 29.12) (3.16227 \dots w - 29.12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3.16227 \dots w + 29.12 = 0 or 3.16227 \dots w - 29.12 = 0

Solve

3.16227 \dots w + 29.12 = 0 : w = - 9.20855 \dots

Solve

3.16227 \dots w - 29.12 = 0 : w = 9.20855 \dots

The solutions to the quadratic equation are:

w = - 9.20855 \dots, w = 9.20855 \dots

x^{2} - 88 = 12

x^{2} + 10 = 91

x, x^{2} - 2 x y^{2} + y = 1

x, f (x - 1) = x^{2} + 2

4 x^{2} + 5 = 2 x^{2} + 20

What are the solutions to the equation 29.12^2=w^2+(3w)^2 ?
The solutions to the equation 29.12^2=w^2+(3w)^2 are w=-9.20855…,w=9.20855…
Find the zeros of 29.12^2=w^2+(3w)^2
The zeros of 29.12^2=w^2+(3w)^2 are w=-9.20855…,w=9.20855…