Solve x=6sqrt{8}-4sqrt{128}+3sqrt{18}

$$x=6 \sqrt{ 8 } -4 \sqrt{ 128 } +3 \sqrt{ 18 }$$

Solve for x

$$x=-11\sqrt{2}\approx -15.556349186$$

Steps for Solving Linear Equation

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$x=6\times 2\sqrt{2}-4\sqrt{128}+3\sqrt{18}$$

Multiply 6 and 2 to get 12.

$$x=12\sqrt{2}-4\sqrt{128}+3\sqrt{18}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$x=12\sqrt{2}-4\times 8\sqrt{2}+3\sqrt{18}$$

Multiply -4 and 8 to get -32.

$$x=12\sqrt{2}-32\sqrt{2}+3\sqrt{18}$$

Combine 12\sqrt{2} and -32\sqrt{2} to get -20\sqrt{2}.

$$x=-20\sqrt{2}+3\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$x=-20\sqrt{2}+3\times 3\sqrt{2}$$

Multiply 3 and 3 to get 9.

$$x=-20\sqrt{2}+9\sqrt{2}$$

Combine -20\sqrt{2} and 9\sqrt{2} to get -11\sqrt{2}.

$$x=-11\sqrt{2}$$

Assign x

$$x≔-11\sqrt{2}$$