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72=2x^(2) What are the solutions to the given equation? Choose 1 answer: (A) x=6 only (B) x=-6 and x=6 (C) x=-2+6sqrt2 (D) {:[x=-2-6sqrt2" and "],[x=-2+6sqrt2]:}

72=2x2 72=2 x^{2} \newlineWhat are the solutions to the given equation?\newlineChoose 11 answer:\newline(A) x=6 x=6 only\newline(B) x=−6 x=-6 and x=6 x=6 \newline(C) x=−2+62 x=-2+6 \sqrt{2} \newline(D) x=−2−62 x=-2-6 \sqrt{2} and x=−2+62 x=-2+6 \sqrt{2}

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Q. 72=2x2 72=2 x^{2} \newlineWhat are the solutions to the given equation?\newlineChoose 11 answer:\newline(A) x=6 x=6 only\newline(B) x=−6 x=-6 and x=6 x=6 \newline(C) x=−2+62 x=-2+6 \sqrt{2} \newline(D) x=−2−62 x=-2-6 \sqrt{2} and x=−2+62 x=-2+6 \sqrt{2}
  1. Write and Simplify Equation: Write down the given equation and simplify it by dividing both sides by 22 to isolate the x2x^2 term.\newline72=2x272 = 2x^2\newlineDivide both sides by 22:\newline722=2x22\frac{72}{2} = \frac{2x^2}{2}\newline36=x236 = x^2
  2. Solve for x: Solve for x by taking the square root of both sides of the equation.\newlineSince x2=36x^2 = 36, we take the square root of both sides:\newlinex2=36\sqrt{x^2} = \sqrt{36}\newlinex=±6x = \pm 6
  3. Check Solutions: Check the solutions in the original equation to ensure they are correct.\newlineSubstitute x=6x = 6 into the original equation:\newline72=2(6)272 = 2(6)^2\newline72=2(36)72 = 2(36)\newline72=7272 = 72 (True)\newlineSubstitute x=−6x = -6 into the original equation:\newline72=2(−6)272 = 2(-6)^2\newline72=2(36)72 = 2(36)\newline72=7272 = 72 (True)

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