Question

$${ \left(x+6 \right) }^{ 2 } = { \left(15-x \right) }^{ 2 }$$

Answer

x=9/2

Solution


Expand.
\[{x}^{2}+12x+36=225-30x+{x}^{2}\]
Cancel \({x}^{2}\) on both sides.
\[12x+36=225-30x\]
Subtract \(36\) from both sides.
\[12x=225-30x-36\]
Simplify  \(225-30x-36\)  to  \(-30x+189\).
\[12x=-30x+189\]
Add \(30x\) to both sides.
\[12x+30x=189\]
Simplify  \(12x+30x\)  to  \(42x\).
\[42x=189\]
Divide both sides by \(42\).
\[x=\frac{189}{42}\]
Simplify  \(\frac{189}{42}\)  to  \(\frac{9}{2}\).
\[x=\frac{9}{2}\]

Decimal Form: 4.5