Solve 64*10^4=48*10^4+x^2

$$64 \times 10 ^ { 4 } = 48 \times 10 ^ { 4 } + x ^ { 2 }$$

Solve for x

$$x=400$$

$$x=-400$$

Steps Using Difference of Squares

Calculate 10 to the power of 4 and get 10000.

$$64\times 10000=48\times 10^{4}+x^{2}$$

Multiply 64 and 10000 to get 640000.

$$640000=48\times 10^{4}+x^{2}$$

Calculate 10 to the power of 4 and get 10000.

$$640000=48\times 10000+x^{2}$$

Multiply 48 and 10000 to get 480000.

$$640000=480000+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$480000+x^{2}=640000$$

Subtract 640000 from both sides.

$$480000+x^{2}-640000=0$$

Subtract 640000 from 480000 to get -160000.

$$-160000+x^{2}=0$$

Consider -160000+x^{2}. Rewrite -160000+x^{2} as x^{2}-400^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-400\right)\left(x+400\right)=0$$

To find equation solutions, solve x-400=0 and x+400=0.

$$x=400 x=-400$$

Steps by Finding Square Root

Calculate 10 to the power of 4 and get 10000.

$$64\times 10000=48\times 10^{4}+x^{2}$$

Multiply 64 and 10000 to get 640000.

$$640000=48\times 10^{4}+x^{2}$$

Calculate 10 to the power of 4 and get 10000.

$$640000=48\times 10000+x^{2}$$

Multiply 48 and 10000 to get 480000.

$$640000=480000+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$480000+x^{2}=640000$$

Subtract 480000 from both sides.

$$x^{2}=640000-480000$$

Subtract 480000 from 640000 to get 160000.

$$x^{2}=160000$$

Take the square root of both sides of the equation.

$$x=400 x=-400$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 4 and get 10000.

$$64\times 10000=48\times 10^{4}+x^{2}$$

Multiply 64 and 10000 to get 640000.

$$640000=48\times 10^{4}+x^{2}$$

Calculate 10 to the power of 4 and get 10000.

$$640000=48\times 10000+x^{2}$$

Multiply 48 and 10000 to get 480000.

$$640000=480000+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$480000+x^{2}=640000$$

Subtract 640000 from both sides.

$$480000+x^{2}-640000=0$$

Subtract 640000 from 480000 to get -160000.

$$-160000+x^{2}=0$$

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.

$$x^{2}-160000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -160000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-160000\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-160000\right)}}{2}$$

Multiply -4 times -160000.

$$x=\frac{0±\sqrt{640000}}{2}$$

Take the square root of 640000.

$$x=\frac{0±800}{2}$$

Now solve the equation x=\frac{0±800}{2} when ± is plus. Divide 800 by 2.

$$x=400$$

Now solve the equation x=\frac{0±800}{2} when ± is minus. Divide -800 by 2.

$$x=-400$$

The equation is now solved.

$$x=400 x=-400$$