Solve for x
x=7
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2\times 2\sqrt{10}+3\sqrt{10}=x\sqrt{10}
Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.
4\sqrt{10}+3\sqrt{10}=x\sqrt{10}
Multiply 2 and 2 to get 4.
7\sqrt{10}=x\sqrt{10}
Combine 4\sqrt{10} and 3\sqrt{10} to get 7\sqrt{10}.
x\sqrt{10}=7\sqrt{10}
Swap sides so that all variable terms are on the left hand side.
\sqrt{10}x=7\sqrt{10}
The equation is in standard form.
\frac{\sqrt{10}x}{\sqrt{10}}=\frac{7\sqrt{10}}{\sqrt{10}}
Divide both sides by \sqrt{10}.
x=\frac{7\sqrt{10}}{\sqrt{10}}
Dividing by \sqrt{10} undoes the multiplication by \sqrt{10}.
x=7
Divide 7\sqrt{10} by \sqrt{10}.
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