Solve 6.37^3/1=22.4^3/T^2

$$\frac { 6.37 ^ { 3 } } { 1 } = \frac { 22.4 ^ { 3 } } { T ^ { 2 } }$$

Solve for T

$$T = \frac{2560 \sqrt{455}}{8281} \approx 6.5942116$$

$$T = -\frac{2560 \sqrt{455}}{8281} \approx -6.5942116$$

Steps by Finding Square Root

Variable T cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by T^{2}.

$$T^{2}\times 6.37^{3}=22.4^{3}$$

Calculate 6.37 to the power of 3 and get 258.474853.

$$T^{2}\times 258.474853=22.4^{3}$$

Calculate 22.4 to the power of 3 and get 11239.424.

$$T^{2}\times 258.474853=11239.424$$

Divide both sides by 258.474853.

$$T^{2}=\frac{11239.424}{258.474853}$$

Expand \frac{11239.424}{258.474853} by multiplying both numerator and the denominator by 1000000.

$$T^{2}=\frac{11239424000}{258474853}$$

Reduce the fraction \frac{11239424000}{258474853} to lowest terms by extracting and canceling out 343.

$$T^{2}=\frac{32768000}{753571}$$

Take the square root of both sides of the equation.

$$T=\frac{2560\sqrt{455}}{8281} T=-\frac{2560\sqrt{455}}{8281}$$

Steps Using the Quadratic Formula

Variable T cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by T^{2}.

$$T^{2}\times 6.37^{3}=22.4^{3}$$

Calculate 6.37 to the power of 3 and get 258.474853.

$$T^{2}\times 258.474853=22.4^{3}$$

Calculate 22.4 to the power of 3 and get 11239.424.

$$T^{2}\times 258.474853=11239.424$$

Subtract 11239.424 from both sides.

$$T^{2}\times 258.474853-11239.424=0$$

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.

$$258.474853T^{2}-11239.424=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 258.474853 for a, 0 for b, and -11239.424 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$T=\frac{0±\sqrt{0^{2}-4\times 258.474853\left(-11239.424\right)}}{2\times 258.474853}$$

Square 0.

$$T=\frac{0±\sqrt{-4\times 258.474853\left(-11239.424\right)}}{2\times 258.474853}$$

Multiply -4 times 258.474853.

$$T=\frac{0±\sqrt{-1033.899412\left(-11239.424\right)}}{2\times 258.474853}$$

Multiply -1033.899412 times -11239.424 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$T=\frac{0±\sqrt{11620433.864818688}}{2\times 258.474853}$$

Take the square root of 11620433.864818688.

$$T=\frac{0±\frac{499408\sqrt{455}}{3125}}{2\times 258.474853}$$

Multiply 2 times 258.474853.

$$T=\frac{0±\frac{499408\sqrt{455}}{3125}}{516.949706}$$

Now solve the equation T=\frac{0±\frac{499408\sqrt{455}}{3125}}{516.949706} when ± is plus.

$$T=\frac{2560\sqrt{455}}{8281}$$

Now solve the equation T=\frac{0±\frac{499408\sqrt{455}}{3125}}{516.949706} when ± is minus.

$$T=-\frac{2560\sqrt{455}}{8281}$$

The equation is now solved.

$$T=\frac{2560\sqrt{455}}{8281} T=-\frac{2560\sqrt{455}}{8281}$$