Let p=4x-7. Which equation is equivalent to (4x-7)^(2)+16=40 x-70 in terms of p ? Choose 1 answer: (A) p^(2)-10 p+86=0 (B) p^(2)-10 p+16=0 (C) p^(2)+10 p+86=0 (D) p^(2)+10 p+16=0

Substitute p in equation: Substitute p for 4x-7 in the given equation. Given equation: (4x-7)² + 16 = 40x - 70 Substitute p for 4x-7: p² + 16 = 40x - 70Express 40x in terms of p: Express 40x in terms of p. We know that p = 4x - 7, so 4x = p + 7. Substitute 4x in the equation: p² + 16 = 40(p + 7) - 70Distribute and simplify equation: Distribute and simplify the equation. p² + 16 = 40p + 280 - 70 p² + 16 = 40p + 210Move terms to set equation to zero: Move all terms to one side to set the equation to zero. p² - 40p + 16 = 210 p² - 40p + 16 - 210 = 0 p² - 40p - 194 = 0Check answer choices: Check the given answer choices to see which one matches the simplified equation. The simplified equation is p² - 40p - 194 = 0, but none of the answer choices match this equation. There seems to be a mistake in the simplification process.

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Let
p=4x-7.
Which equation is equivalent to
(4x-7)^(2)+16=40 x-70 in terms of
p ?
Choose 1 answer:
(A)
p^(2)-10 p+86=0
(B)
p^(2)-10 p+16=0
(C)
p^(2)+10 p+86=0
(D)
p^(2)+10 p+16=0

Let $p=4x-7$ . Which equation is equivalent to $(4x-7)^{2}+16=40x-70$ in terms of $p$ ? Choose $1$ answer: $\newline$ (A) $p^{2}-10p+86=0$ $\newline$ (B) $p^{2}-10p+16=0$ $\newline$ (C) $p^{2}+10p+86=0$ $\newline$ (D) $p^{2}+10p+16=0$

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Math Problems

Algebra 1

Solve a quadratic equation by factoring

Full solution

Q. Let

p=4x-7

. Which equation is equivalent to

(4x-7)^{2}+16=40x-70

in terms of

p

? Choose

1

answer:

\newline

(A)

p^{2}-10p+86=0

\newline

(B)

p^{2}-10p+16=0

\newline

(C)

p^{2}+10p+86=0

\newline

(D)

p^{2}+10p+16=0

Substitute $p$ in equation: Substitute $p$ for $4x-7$ in the given equation. $\newline$ Given equation: $(4x-7)^2 + 16 = 40x - 70$ $\newline$ Substitute $p$ for $4x-7$ : $p^2 + 16 = 40x - 70$
Express $40x$ in terms of $p$ : Express $40x$ in terms of $p$ .
We know that $p = 4x - 7$ , so $4x = p + 7$ .
Substitute $4x$ in the equation: $p^2 + 16 = 40(p + 7) - 70$
Distribute and simplify equation: Distribute and simplify the equation. $\newline$ $p^2 + 16 = 40p + 280 - 70$ $\newline$ $p^2 + 16 = 40p + 210$
Move terms to set equation to zero: Move all terms to one side to set the equation to zero. $\newline$ $p^2 - 40p + 16 = 210$ $\newline$ $p^2 - 40p + 16 - 210 = 0$ $\newline$ $p^2 - 40p - 194 = 0$
Check answer choices: Check the given answer choices to see which one matches the simplified equation. $\newline$ The simplified equation is $p^2 - 40p - 194 = 0$ , but none of the answer choices match this equation. There seems to be a mistake in the simplification process.