Solve 2.6^2=1^2+x^2

$${ 2.6 }^{ 2 } = { 1 }^{ 2 } + { x }^{ 2 }$$

Solve for x

$$x=2.4$$

$$x=-2.4$$

Steps Using Difference of Squares

Calculate 2.6 to the power of 2 and get 6.76.

$$6.76=1^{2}+x^{2}$$

Calculate 1 to the power of 2 and get 1.

$$6.76=1+x^{2}$$

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

$$1+x^{2}=6.76$$

Subtract 6.76 from both sides.

$$1+x^{2}-6.76=0$$

Subtract 6.76 from 1 to get -5.76.

$$-5.76+x^{2}=0$$

Consider -5.76+x^{2}. Rewrite -5.76+x^{2} as x^{2}-\left(\frac{12}{5}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-\frac{12}{5}\right)\left(x+\frac{12}{5}\right)=0$$

To find equation solutions, solve x-\frac{12}{5}=0 and x+\frac{12}{5}=0.

$$x=\frac{12}{5} x=-\frac{12}{5}$$

Steps by Finding Square Root

Calculate 2.6 to the power of 2 and get 6.76.

$$6.76=1^{2}+x^{2}$$

Calculate 1 to the power of 2 and get 1.

$$6.76=1+x^{2}$$

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

$$1+x^{2}=6.76$$

Subtract 1 from both sides.

$$x^{2}=6.76-1$$

Subtract 1 from 6.76 to get 5.76.

$$x^{2}=5.76$$

Take the square root of both sides of the equation.

$$x=\frac{12}{5} x=-\frac{12}{5}$$

Steps Using the Quadratic Formula

Calculate 2.6 to the power of 2 and get 6.76.

$$6.76=1^{2}+x^{2}$$

Calculate 1 to the power of 2 and get 1.

$$6.76=1+x^{2}$$

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

$$1+x^{2}=6.76$$

Subtract 6.76 from both sides.

$$1+x^{2}-6.76=0$$

Subtract 6.76 from 1 to get -5.76.

$$-5.76+x^{2}=0$$

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.

$$x^{2}-5.76=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -5.76 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5.76\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5.76\right)}}{2}$$

Multiply -4 times -5.76.

$$x=\frac{0±\sqrt{23.04}}{2}$$

Take the square root of 23.04.

$$x=\frac{0±\frac{24}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{24}{5}}{2} when ± is plus.

$$x=\frac{12}{5}$$

Now solve the equation x=\frac{0±\frac{24}{5}}{2} when ± is minus.

$$x=-\frac{12}{5}$$

The equation is now solved.

$$x=\frac{12}{5} x=-\frac{12}{5}$$