Solve k^2|4|=+40

$$k ^ { 2 } | 4 | = + 40$$

Solve for k

$$k=\sqrt{10}\approx 3.16227766$$

$$k=-\sqrt{10}\approx -3.16227766$$

Steps by Finding Square Root

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 4 is 4.

$$k^{2}\times 4=40$$

Divide both sides by 4.

$$k^{2}=\frac{40}{4}$$

Divide 40 by 4 to get 10.

$$k^{2}=10$$

Take the square root of both sides of the equation.

$$k=\sqrt{10} k=-\sqrt{10}$$

Steps Using the Quadratic Formula

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 4 is 4.

$$k^{2}\times 4=40$$

Subtract 40 from both sides.

$$k^{2}\times 4-40=0$$

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.

$$4k^{2}-40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\times 4\left(-40\right)}}{2\times 4}$$

Square 0.

$$k=\frac{0±\sqrt{-4\times 4\left(-40\right)}}{2\times 4}$$

Multiply -4 times 4.

$$k=\frac{0±\sqrt{-16\left(-40\right)}}{2\times 4}$$

Multiply -16 times -40.

$$k=\frac{0±\sqrt{640}}{2\times 4}$$

Take the square root of 640.

$$k=\frac{0±8\sqrt{10}}{2\times 4}$$

Multiply 2 times 4.

$$k=\frac{0±8\sqrt{10}}{8}$$

Now solve the equation k=\frac{0±8\sqrt{10}}{8} when ± is plus.

$$k=\sqrt{10}$$

Now solve the equation k=\frac{0±8\sqrt{10}}{8} when ± is minus.

$$k=-\sqrt{10}$$

The equation is now solved.

$$k=\sqrt{10} k=-\sqrt{10}$$