Question

$$2(4x \times 2x+4x \times x+2x \times x)=700$$

Answer

x=5,-5

Solution


Take out the constants.
\[2((4\times 2)xx+4xx+2xx)=700\]
Simplify  \(4\times 2\)  to  \(8\).
\[2(8xx+4xx+2xx)=700\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[2(8{x}^{2}+4xx+2xx)=700\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[2(8{x}^{2}+4{x}^{2}+2xx)=700\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[2(8{x}^{2}+4{x}^{2}+2{x}^{2})=700\]
Simplify  \(8{x}^{2}+4{x}^{2}+2{x}^{2}\)  to  \(14{x}^{2}\).
\[2\times 14{x}^{2}=700\]
Simplify  \(2\times 14{x}^{2}\)  to  \(28{x}^{2}\).
\[28{x}^{2}=700\]
Divide both sides by \(28\).
\[{x}^{2}=\frac{700}{28}\]
Simplify  \(\frac{700}{28}\)  to  \(25\).
\[{x}^{2}=25\]
Take the square root of both sides.
\[x=\pm \sqrt{25}\]
Since \(5\times 5=25\), the square root of \(25\) is \(5\).
\[x=\pm 5\]