Solve 5/14x^2=43/8

$$\frac { 5 } { 14 } x ^ { 2 } = 4 \frac { 3 } { 8 }$$

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

Multiply both sides of the equation by 56, the least common multiple of 14,8.

$$20x^{2}=7\left(4\times 8+3\right)$$

Multiply 4 and 8 to get 32.

$$20x^{2}=7\left(32+3\right)$$

Add 32 and 3 to get 35.

$$20x^{2}=7\times 35$$

Multiply 7 and 35 to get 245.

$$20x^{2}=245$$

Subtract 245 from both sides.

$$20x^{2}-245=0$$

Divide both sides by 5.

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

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

Multiply both sides of the equation by 56, the least common multiple of 14,8.

$$20x^{2}=7\left(4\times 8+3\right)$$

Multiply 4 and 8 to get 32.

$$20x^{2}=7\left(32+3\right)$$

Add 32 and 3 to get 35.

$$20x^{2}=7\times 35$$

Multiply 7 and 35 to get 245.

$$20x^{2}=245$$

Divide both sides by 20.

$$x^{2}=\frac{245}{20}$$

Reduce the fraction \frac{245}{20} to lowest terms by extracting and canceling out 5.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Multiply both sides of the equation by 56, the least common multiple of 14,8.

$$20x^{2}=7\left(4\times 8+3\right)$$

Multiply 4 and 8 to get 32.

$$20x^{2}=7\left(32+3\right)$$

Add 32 and 3 to get 35.

$$20x^{2}=7\times 35$$

Multiply 7 and 35 to get 245.

$$20x^{2}=245$$

Subtract 245 from both sides.

$$20x^{2}-245=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and -245 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 20\left(-245\right)}}{2\times 20}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 20\left(-245\right)}}{2\times 20}$$

Multiply -4 times 20.

$$x=\frac{0±\sqrt{-80\left(-245\right)}}{2\times 20}$$

Multiply -80 times -245.

$$x=\frac{0±\sqrt{19600}}{2\times 20}$$

Take the square root of 19600.

$$x=\frac{0±140}{2\times 20}$$

Multiply 2 times 20.

$$x=\frac{0±140}{40}$$

Now solve the equation x=\frac{0±140}{40} when ± is plus. Reduce the fraction \frac{140}{40} to lowest terms by extracting and canceling out 20.

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

Now solve the equation x=\frac{0±140}{40} when ± is minus. Reduce the fraction \frac{-140}{40} to lowest terms by extracting and canceling out 20.

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

The equation is now solved.

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