Solve 0=2x^2 8w-2170

Question

Solve the equation

Solve for x

Solve for w

w \neq = 0, x = - \frac{2170 w}{4 ∣ w ∣} w \neq = 0, x = \frac{2170 w}{4 ∣ w ∣}

Evaluate

0 = 2 x^{2} \times 8 w - 2170

Multiply the terms

0 = 16 x^{2} w - 2170

Rewrite the expression

0 = 16 w x^{2} - 2170

Swap the sides of the equation

16 w x^{2} - 2170 = 0

Move the constant to the right-hand side and change its sign

16 w x^{2} = 0 + 2170

Removing 0 doesn't change the value,so remove it from the expression

16 w x^{2} = 2170

Divide both sides

\frac{16 w x ^{2}}{16 w} = \frac{2170}{16 w}

Divide the numbers

x^{2} = \frac{2170}{16 w}

Cancel out the common factor 2

x^{2} = \frac{1085}{8 w}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{1085}{8 w}

Simplify the expression

More Steps

Evaluate

\frac{1085}{8 w}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1085}{8 w}

Simplify the radical expression

More Steps

Evaluate

8 w

Rewrite the expression

8 \times w

Simplify the root

2 2 w

\frac{1085}{2 2 w}

Multiply by the Conjugate

\frac{1085 \times 2 w}{2 2 w \times 2 w}

Calculate

\frac{1085 \times 2 w}{2 \times 2 ∣ w ∣}

Calculate

More Steps

Evaluate

1085 \times 2 w

The product of roots with the same index is equal to the root of the product

1085 \times 2 w

Calculate the product

2170 w

\frac{2170 w}{2 \times 2 ∣ w ∣}

Calculate

\frac{2170 w}{4 ∣ w ∣}

x = \pm \frac{2170 w}{4 ∣ w ∣}

Separate the equation into 2 possible cases

x = \frac{2170 w}{4 ∣ w ∣} x = - \frac{2170 w}{4 ∣ w ∣}

Calculate

{w \neq = 0 x = - \frac{2170 w}{4 ∣ w ∣} {w \neq = 0 x = \frac{2170 w}{4 ∣ w ∣}

Solution

w \neq = 0, x = - \frac{2170 w}{4 ∣ w ∣} w \neq = 0, x = \frac{2170 w}{4 ∣ w ∣}

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