Solve 4(6.5)=sqrt{56c6.5-312}

$$4 ( 6.5 ) = \sqrt { 56 c 6.5 - 312 }$$

Solve for c_6

$$c_{6} = \frac{247}{7} = 35\frac{2}{7} \approx 35.285714286$$

Steps for Solving Radical Equations

Multiply 4 and 6.5 to get 26.

$$26=\sqrt{56c_{6}\times 0.5-312}$$

Multiply 56 and 0.5 to get 28.

$$26=\sqrt{28c_{6}-312}$$

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

$$\sqrt{28c_{6}-312}=26$$

Square both sides of the equation.

$$28c_{6}-312=676$$

Add 312 to both sides of the equation.

$$28c_{6}-312-\left(-312\right)=676-\left(-312\right)$$

Subtracting -312 from itself leaves 0.

$$28c_{6}=676-\left(-312\right)$$

Subtract -312 from 676.

$$28c_{6}=988$$

Divide both sides by 28.

$$\frac{28c_{6}}{28}=\frac{988}{28}$$

Dividing by 28 undoes the multiplication by 28.

$$c_{6}=\frac{988}{28}$$

Reduce the fraction \frac{988}{28} to lowest terms by extracting and canceling out 4.

$$c_{6}=\frac{247}{7}$$