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Let m=5x-2. Which equation is equivalent to (5x-2)^(2)+35 x-14=-12 in terms of m ? Choose 1 answer: (A) m^(2)-7m-2=0 (B) m^(2)-7m+12=0 (C) m^(2)+7m-2=0 (D) m^(2)+7m+12=0

Let m=5x−2m=5x-2. Which equation is equivalent to (5x−2)2+35x−14=−12(5x-2)^{2}+35x-14=-12 in terms of mm? Choose 11 answer:\newline(A) m2−7m−2=0m^{2}-7m-2=0\newline(B) m2−7m+12=0m^{2}-7m+12=0\newline(C) m2+7m−2=0m^{2}+7m-2=0\newline(D) m2+7m+12=0m^{2}+7m+12=0

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Full solution

Q. Let m=5x−2m=5x-2. Which equation is equivalent to (5x−2)2+35x−14=−12(5x-2)^{2}+35x-14=-12 in terms of mm? Choose 11 answer:\newline(A) m2−7m−2=0m^{2}-7m-2=0\newline(B) m2−7m+12=0m^{2}-7m+12=0\newline(C) m2+7m−2=0m^{2}+7m-2=0\newline(D) m2+7m+12=0m^{2}+7m+12=0
  1. Expand (5x−2)2(5x-2)^2: We are given that m=5x−2m = 5x - 2. We need to express the equation (5x−2)2+35x−14=−12(5x-2)^2 + 35x - 14 = -12 in terms of mm.\newlineFirst, let's expand (5x−2)2(5x-2)^2.\newline(5x−2)2=(5x−2)(5x−2)=25x2−10x−10x+4=25x2−20x+4(5x-2)^2 = (5x-2)(5x-2) = 25x^2 - 10x - 10x + 4 = 25x^2 - 20x + 4
  2. Substitute expanded form into equation: Now, let's substitute the expanded form of (5x−2)2(5x-2)^2 into the original equation.25x2−20x+4+35x−14=−1225x^2 - 20x + 4 + 35x - 14 = -12
  3. Combine like terms: Combine like terms in the equation. 25x2+15x−10=−1225x^2 + 15x - 10 = -12
  4. Set equation to zero: Add 1212 to both sides to set the equation to zero.\newline25x2+15x−10+12=025x^2 + 15x - 10 + 12 = 0\newline25x2+15x+2=025x^2 + 15x + 2 = 0
  5. Substitute mm back into equation: Now, we need to express this equation in terms of mm. Recall that m=5x−2m = 5x - 2.\newlineLet's substitute 5x−25x - 2 back in for mm.\newlinem2+35x−14=−12m^2 + 35x - 14 = -12
  6. Solve for x: We need to express 35x35x in terms of mm. Since m=5x−2m = 5x - 2, we can solve for xx: \newline5x=m+25x = m + 2\newlinex=m+25x = \frac{m + 2}{5}
  7. Substitute xx back into equation: Substitute xx back into the equation in terms of mm.m2+35(m+25)−14=−12m^2 + 35\left(\frac{m + 2}{5}\right) - 14 = -12
  8. Distribute 3535 inside parentheses: Distribute the 3535 inside the parentheses.m2+7(m+2)−14=−12m^2 + 7(m + 2) - 14 = -12
  9. Expand the equation: Expand the equation. m2+7m+14−14=−12m^2 + 7m + 14 - 14 = -12
  10. Combine like terms: Combine like terms. m2+7m=−12m^2 + 7m = -12
  11. Set equation to zero: Add 1212 to both sides to set the equation to zero.\newlinem2+7m+12=0m^2 + 7m + 12 = 0

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