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Let p=3x+4. Which equation is equivalent to (3x+4)^(2)-36=15 x+20 in terms of p ? Choose 1 answer: (A) p^(2)+5p-56=0 (B) p^(2)-5p-36=0 (C) p^(2)+5p-36=0 (D) p^(2)-5p-56=0

Let p=3x+4 p=3x+4 . Which equation is equivalent to (3x+4)2−36=15x+20 (3x+4)^{2}-36=15x+20 in terms of p p ? Choose 11 answer:\newline(A) p2+5p−56=0 p^{2}+5p-56=0 \newline(B) p2−5p−36=0 p^{2}-5p-36=0 \newline(C) p2+5p−36=0 p^{2}+5p-36=0 \newline(D) p2−5p−56=0 p^{2}-5p-56=0

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Full solution

Q. Let p=3x+4 p=3x+4 . Which equation is equivalent to (3x+4)2−36=15x+20 (3x+4)^{2}-36=15x+20 in terms of p p ? Choose 11 answer:\newline(A) p2+5p−56=0 p^{2}+5p-56=0 \newline(B) p2−5p−36=0 p^{2}-5p-36=0 \newline(C) p2+5p−36=0 p^{2}+5p-36=0 \newline(D) p2−5p−56=0 p^{2}-5p-56=0
  1. Given equation: We are given that p=3x+4 p = 3x + 4 . We need to express the equation (3x+4)2−36=15x+20 (3x+4)^2 - 36 = 15x + 20 in terms of p p .\newlineFirst, let's expand (3x+4)2 (3x+4)^2 .\newline(3x+4)2=(3x+4)(3x+4)=9x2+12x+12x+16=9x2+24x+16 (3x+4)^2 = (3x+4)(3x+4) = 9x^2 + 12x + 12x + 16 = 9x^2 + 24x + 16
  2. Expanding (3x+4)2(3x+4)^2: Now, let's substitute the expanded form of (3x+4)2(3x+4)^2 into the given equation.\newline9x2+24x+16−36=15x+209x^2 + 24x + 16 - 36 = 15x + 20
  3. Substituting into given equation: Next, we simplify the left side of the equation by subtracting 3636 from both sides.\newline9x2+24x+16−36=15x+209x^2 + 24x + 16 - 36 = 15x + 20\newline9x2+24x−20=15x+209x^2 + 24x - 20 = 15x + 20
  4. Simplifying left side: Now, we subtract 15x15x from both sides to get the xx terms on one side.\newline9x2+24x−20−15x=15x+20−15x9x^2 + 24x - 20 - 15x = 15x + 20 - 15x\newline9x2+9x−20=209x^2 + 9x - 20 = 20
  5. Isolating x terms: Next, we subtract 2020 from both sides to isolate the terms with xx on one side.\newline9x2+9x−20−20=20−209x^2 + 9x - 20 - 20 = 20 - 20\newline9x2+9x−40=09x^2 + 9x - 40 = 0
  6. Subtracting 2020: Now, we need to express this equation in terms of pp. Since p=3x+4p = 3x + 4, we can rewrite 9x9x as 3(3x)3(3x) and 9x29x^2 as \ (\(3x)^22 \\).(3x)2+3(3x)−40=0 (3x)^2 + 3(3x) - 40 = 0
  7. Expressing in terms of p p : Substitute p p for 3x+4 3x + 4 in the equation.\newline(p−4)2+3(p−4)−40=0 (p - 4)^2 + 3(p - 4) - 40 = 0
  8. Substituting p p for 3x+4 3x + 4 : Expand (p−4)2 (p - 4)^2 and simplify the equation.\newline(p−4)(p−4)+3p−12−40=0 (p - 4)(p - 4) + 3p - 12 - 40 = 0 \newlinep2−4p−4p+16+3p−12−40=0 p^2 - 4p - 4p + 16 + 3p - 12 - 40 = 0 \newlinep2−5p+16−12−40=0 p^2 - 5p + 16 - 12 - 40 = 0
  9. Expanding (p−4)2(p - 4)^2: Combine like terms to simplify the equation further.\newlinep2−8p+16−52=0p^2 - 8p + 16 - 52 = 0\newlinep2−8p−36=0p^2 - 8p - 36 = 0

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