Solve \sqrt (8x - 23) - 10 = -3

Evaluate

8 x - 23 - 10 = - 3

Find the domain

More Steps

8 x - 23 - 10 = - 3, x \geq \frac{23}{8}

Move the constant to the right-hand side and change its sign

8 x - 23 = - 3 + 10

Add the numbers

8 x - 23 = 7

Raise both sides of the equation to the 2 -th power to eliminate the isolated 2 -th root

(8 x - 23)^{2} = 7^{2}

Evaluate the power

8 x - 23 = 49

Move the constant to the right-hand side and change its sign

8 x = 49 + 23

Add the numbers

8 x = 72

Divide both sides

\frac{8 x}{8} = \frac{72}{8}

Divide the numbers

x = \frac{72}{8}

Divide the numbers

More Steps

x = 9

Check if the solution is in the defined range

x = 9, x \geq \frac{23}{8}

Find the intersection of the solution and the defined range

x = 9

Solution

More Steps

x = 9

\sqrt (8x 23) 10 = 3