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Let m=6x+5. Which equation is equivalent to (6x+5)^(2)-10=-18 x-15 in terms of m ? Choose 1 answer: (A) m^(2)-3m+5=0 (B) m^(2)+3m+5=0 (c) m^(2)-3m-10=0 (D) m^(2)+3m-10=0

Let m=6x+5m=6x+5. Which equation is equivalent to (6x+5)2−10=−18x−15(6x+5)^{2}-10=-18x-15 in terms of mm? Choose 11 answer: (A) m2−3m+5=0m^{2}-3m+5=0 (B) m2+3m+5=0m^{2}+3m+5=0 (C) m2−3m−10=0m^{2}-3m-10=0 (D) m2+3m−10=0m^{2}+3m-10=0

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Full solution

Q. Let m=6x+5m=6x+5. Which equation is equivalent to (6x+5)2−10=−18x−15(6x+5)^{2}-10=-18x-15 in terms of mm? Choose 11 answer: (A) m2−3m+5=0m^{2}-3m+5=0 (B) m2+3m+5=0m^{2}+3m+5=0 (C) m2−3m−10=0m^{2}-3m-10=0 (D) m2+3m−10=0m^{2}+3m-10=0
  1. Substitute mm: Let's first substitute mm for 6x+56x+5 in the given equation.\newline(6x+5)2−10=−18x−15(6x+5)^2 - 10 = -18x - 15\newlineSubstitute mm:\newlinem2−10=−18x−15m^2 - 10 = -18x - 15
  2. Express −18x-18x in terms of mm: Now, we need to express −18x-18x in terms of mm. Since m=6x+5m = 6x + 5, we can solve for xx:6x=m−56x = m - 5x=m−56x = \frac{m - 5}{6}
  3. Substitute xx back: Substitute xx back into the equation: m2−10=−18(m−56)−15m^2 - 10 = -18\left(\frac{m - 5}{6}\right) - 15
  4. Simplify the equation: Simplify the equation by multiplying −18-18 with (m−5)/6(m - 5)/6:m2−10=−3(m−5)−15m^2 - 10 = -3(m - 5) - 15
  5. Distribute −3-3 inside: Distribute −3-3 inside the parentheses: m2−10=−3m+15−15m^2 - 10 = -3m + 15 - 15
  6. Combine like terms: Combine like terms: m2−10=−3mm^2 - 10 = -3m
  7. Add 1010 to both sides: Add 1010 to both sides to set the equation to zero:\newlinem2−3m=0m^2 - 3m = 0
  8. Correct the substitution: None of the answer choices match m2−3m=0m^2 - 3m = 0 exactly, so we must have made a mistake. Let's go back and check our steps.
  9. Distribute −3-3 correctly: Let's correct the substitution and multiplication:\newlinem2−10=−18(m−56)−15m^2 - 10 = -18\left(\frac{m - 5}{6}\right) - 15\newlineSimplify the right side:\newlinem2−10=−3(m−5)−15m^2 - 10 = -3(m - 5) - 15
  10. Combine like terms: Now distribute −3-3 inside the parentheses correctly: m2−10=−3m+15−15m^2 - 10 = -3m + 15 - 15
  11. Add 1010 to both sides: Combine like terms on the right side:\newlinem2−10=−3mm^2 - 10 = -3m
  12. Correct the final step: Now, add 1010 to both sides to set the equation to zero:\newlinem2−3m+10=0m^2 - 3m + 10 = 0
  13. Move all terms to one side: Looking at the answer choices, we see that the correct equivalent equation in terms of mm is: m2−3m+10=0m^2 - 3m + 10 = 0 This matches answer choice (C) m2−3m−10=0m^2 - 3m - 10 = 0, but we have a positive 1010, not a negative 1010. We need to check our steps again.
  14. Move all terms to one side: Looking at the answer choices, we see that the correct equivalent equation in terms of mm is: m2−3m+10=0m^2 - 3m + 10 = 0 This matches answer choice (C) m2−3m−10=0m^2 - 3m - 10 = 0, but we have a positive 1010, not a negative 1010. We need to check our steps again.Let's correct the final step: m2−10=−3mm^2 - 10 = -3m Add 1010 to both sides: m2=−3m+10m^2 = -3m + 10
  15. Move all terms to one side: Looking at the answer choices, we see that the correct equivalent equation in terms of mm is: m2−3m+10=0m^2 - 3m + 10 = 0 This matches answer choice (C) m2−3m−10=0m^2 - 3m - 10 = 0, but we have a positive 1010, not a negative 1010. We need to check our steps again.Let's correct the final step: m2−10=−3mm^2 - 10 = -3m Add 1010 to both sides: m2=−3m+10m^2 = -3m + 10Now, we need to move all terms to one side to set the equation to zero: m2+3m−10=0m^2 + 3m - 10 = 0
  16. Move all terms to one side: Looking at the answer choices, we see that the correct equivalent equation in terms of mm is: m2−3m+10=0m^2 - 3m + 10 = 0 This matches answer choice (C) m2−3m−10=0m^2 - 3m - 10 = 0, but we have a positive 1010, not a negative 1010. We need to check our steps again.Let's correct the final step: m2−10=−3mm^2 - 10 = -3m Add 1010 to both sides: m2=−3m+10m^2 = -3m + 10Now, we need to move all terms to one side to set the equation to zero: m2+3m−10=0m^2 + 3m - 10 = 0Looking at the answer choices, we see that the correct equivalent equation in terms of mm is: m2+3m−10=0m^2 + 3m - 10 = 0 This matches answer choice (D).

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