Solve 8x^2-98=0

$$8 { x }^{ 2 } -98=0$$

Solve for x

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

$$x = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

Steps Using Difference of Squares

Divide both sides by 2.

$$4x^{2}-49=0$$

Consider 4x^{2}-49. Rewrite 4x^{2}-49 as \left(2x\right)^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-7\right)\left(2x+7\right)=0$$

To find equation solutions, solve 2x-7=0 and 2x+7=0.

$$x=\frac{7}{2} x=-\frac{7}{2}$$

Steps by Finding Square Root

Add 98 to both sides. Anything plus zero gives itself.

$$8x^{2}=98$$

Divide both sides by 8.

$$x^{2}=\frac{98}{8}$$

Reduce the fraction \frac{98}{8} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{49}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{7}{2} x=-\frac{7}{2}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$8x^{2}-98=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -98 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-98\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-98\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-98\right)}}{2\times 8}$$

Multiply -32 times -98.

$$x=\frac{0±\sqrt{3136}}{2\times 8}$$

Take the square root of 3136.

$$x=\frac{0±56}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±56}{16}$$

Now solve the equation x=\frac{0±56}{16} when ± is plus. Reduce the fraction \frac{56}{16} to lowest terms by extracting and canceling out 8.

$$x=\frac{7}{2}$$

Now solve the equation x=\frac{0±56}{16} when ± is minus. Reduce the fraction \frac{-56}{16} to lowest terms by extracting and canceling out 8.

$$x=-\frac{7}{2}$$

The equation is now solved.

$$x=\frac{7}{2} x=-\frac{7}{2}$$