Let m=x^(2)-5. Which equation is equivalent to (x^(2)-5)^(2)-3x^(2)+15=-2 in terms of m ? Choose 1 answer: (A) m^(2)+3m+2=0 (B) m^(2)+3m+17=0 (c) m^(2)-3m+2=0 (D) m^(2)-3m+17=0

Given equation: We are given m = x^2 - 5. We need to find an equivalent equation for (x^2 - 5)^2 - 3x^2 + 15 = -2 in terms of m. First, let's expand (x^2 - 5)^2. (x^2 - 5)^2 = x^4 - 10x^2 + 25Expanding (x^2 - 5)^2: Now, let's substitute x^2 - 5 with m in the expanded form. m^2 = (x^2 - 5)^2 = x^4 - 10x^2 + 25Substituting x^2 - 5 with m: Next, we substitute m back into the original equation (x^2 - 5)^2 - 3x^2 + 15 = -2. m^2 - 3(x^2) + 15 = -2Substituting m back into the original equation: Since m = x^2 - 5, we can replace x^2 in the equation with m + 5. m^2 - 3(m + 5) + 15 = -2Replacing x^2 with m + 5: Now, distribute the -3 across (m + 5). m^2 - 3m - 15 + 15 = -2Distributing -3 across (m + 5): The +15 and -15 cancel each other out, simplifying the equation to: m^2 - 3m = -2Simplifying the equation: Finally, we add 2 to both sides to set the equation to 0. m^2 - 3m + 2 = 0

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Let
m=x^(2)-5.
Which equation is equivalent to
(x^(2)-5)^(2)-3x^(2)+15=-2 in terms of
m ?
Choose 1 answer:
(A)
m^(2)+3m+2=0
(B)
m^(2)+3m+17=0
(c)
m^(2)-3m+2=0
(D)
m^(2)-3m+17=0

Let $m=x^{2}-5$ . Which equation is equivalent to $(x^{2}-5)^{2}-3x^{2}+15=-2$ in terms of $m$ ? Choose $1$ answer: $\newline$ (A) $m^{2}+3m+2=0$ $\newline$ (B) $m^{2}+3m+17=0$ $\newline$ (C) $m^{2}-3m+2=0$ $\newline$ (D) $m^{2}-3m+17=0$

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Math Problems

Algebra 1

Solve a quadratic equation by factoring

Full solution

Q. Let

m=x^{2}-5

. Which equation is equivalent to

(x^{2}-5)^{2}-3x^{2}+15=-2

in terms of

m

? Choose

1

answer:

\newline

(A)

m^{2}+3m+2=0

\newline

(B)

m^{2}+3m+17=0

\newline

(C)

m^{2}-3m+2=0

\newline

(D)

m^{2}-3m+17=0

Given equation: We are given $m = x^2 - 5$ . We need to find an equivalent equation for $(x^2 - 5)^2 - 3x^2 + 15 = -2$ in terms of $m$ . $\newline$ First, let's expand $(x^2 - 5)^2$ . $\newline$ $(x^2 - 5)^2 = x^4 - 10x^2 + 25$
Expanding $(x^2 - 5)^2$ : Now, let's substitute $x^2 - 5$ with $m$ in the expanded form. $m^2 = (x^2 - 5)^2 = x^4 - 10x^2 + 25$
Substituting $x^2 - 5$ with $m$ : Next, we substitute $m$ back into the original equation $(x^2 - 5)^2 - 3x^2 + 15 = -2$ . $\newline$ $m^2 - 3(x^2) + 15 = -2$
Substituting $m$ back into the original equation: Since $m = x^2 - 5$ , we can replace $x^2$ in the equation with $m + 5$ . $\newline$ $m^2 - 3(m + 5) + 15 = -2$
Replacing $x^2$ with $m + 5$ : Now, distribute the $-3$ across $(m + 5)$ . $\newline$ $m^2 - 3m - 15 + 15 = -2$
Distributing $-3$ across $(m + 5)$ : The $+15$ and $-15$ cancel each other out, simplifying the equation to: $m^2 - 3m = -2$
Simplifying the equation: Finally, we add $2$ to both sides to set the equation to $0$ . $\newline$ $m^2 - 3m + 2 = 0$