Solve the equation for the indicated variable.
-Solve for $x$ : $25 + \sqrt { x ^ { 2 } - y ^ { 2 } } = z$
A) $x = z ^ { 2 } + y ^ { 2 } - 50 z + 625$
B) $x = \pm \sqrt { z + y ^ { 2 } - 5 }$
C) $x = \sqrt { z - y ^ { 2 } - 5 }$
D) $x = \pm \sqrt { ( z - 25 ) ^ { 2 } + y ^ { 2 } }$

Question

Quizplus · Accepted Answer

First, isolate the square root by subtracting 25 from both sides, giving $\sqrt{x^2 - y^2} = z - 25$. Then square both sides to eliminate the square root, resulting in $x^2 - y^2 = (z - 25)^2$. Finally, solve for $x$ by adding $y^2$ to both sides and taking the square root, yielding $x = \pm \sqrt{(z - 25)^2 + y^2}$.

Solve the Equation for the Indicated Variable xxx 25+x2−y2=z25 + \sqrt { x ^ { 2 } - y ^ { 2 } } = z25+x2−y2​=z

Solve the Equation for the Indicated Variable $x$ $25 + \sqrt { x ^ { 2 } - y ^ { 2 } } = z$