Let m=x^(2)+3. Which equation is equivalent to (x^(2)+3)^(2)+7x^(2)+21=-10 in terms of m ? Choose 1 answer: (A) m^(2)-7m+31=0 (B) m^(2)+7m+31=0 (C) m^(2)-7m+10=0 (D) m^(2)+7m+10=0

Substitute m into equation: We are given m = x^(2) + 3. Let's substitute m into the given equation (x^(2)+3)^(2)+7x^(2)+21=-10 to find the equivalent equation in terms of m.Expand and simplify: First, we substitute m for x^(2) + 3 in the equation: (m)^(2) + 7x^(2) + 21 = -10Combine like terms: Since m = x^(2) + 3, we can also substitute m - 3 for x^(2) in the equation: (m)^(2) + 7(m - 3) + 21 = -10Add to both sides: Now, let's expand and simplify the equation: m^(2) + 7m - 21 + 21 = -10Combine like terms: m^(2) + 7m = -10To get the equation in standard form, we add 10 to both sides of the equation: m^(2) + 7m + 10 = 0

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Let
m=x^(2)+3.
Which equation is equivalent to
(x^(2)+3)^(2)+7x^(2)+21=-10 in terms of
m ?
Choose 1 answer:
(A)
m^(2)-7m+31=0
(B)
m^(2)+7m+31=0
(C)
m^(2)-7m+10=0
(D)
m^(2)+7m+10=0

Let $m=x^{2}+3$ . Which equation is equivalent to $(x^{2}+3)^{2}+7x^{2}+21=-10$ in terms of $m$ ? Choose $1$ answer: $\newline$ (A) $m^{2}-7m+31=0$ $\newline$ (B) $m^{2}+7m+31=0$ $\newline$ (C) $m^{2}-7m+10=0$ $\newline$ (D) $m^{2}+7m+10=0$

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Math Problems

Algebra 1

Solve a quadratic equation by factoring

Full solution

Q. Let

m=x^{2}+3

. Which equation is equivalent to

(x^{2}+3)^{2}+7x^{2}+21=-10

in terms of

m

? Choose

1

answer:

\newline

(A)

m^{2}-7m+31=0

\newline

(B)

m^{2}+7m+31=0

\newline

(C)

m^{2}-7m+10=0

\newline

(D)

m^{2}+7m+10=0

Substitute $m$ into equation: We are given $m = x^{2} + 3$ . Let's substitute $m$ into the given equation $(x^{2}+3)^{2}+7x^{2}+21=-10$ to find the equivalent equation in terms of $m$ .
Expand and simplify: First, we substitute $m$ for $x^{2} + 3$ in the equation: $\newline$ $(m)^{2} + 7x^{2} + 21 = -10$
Combine like terms: Since $m = x^{2} + 3$ , we can also substitute $m - 3$ for $x^{2}$ in the equation: $\newline$ $(m)^{2} + 7(m - 3) + 21 = -10$
Add to both sides: Now, let's expand and simplify the equation: $m^{2} + 7m - 21 + 21 = -10$
Add to both sides: Now, let's expand and simplify the equation: $\newline$ $m^2 + 7m - 21 + 21 = -10$ Combine like terms: $\newline$ $m^2 + 7m = -10$
Add to both sides: Now, let's expand and simplify the equation: $\newline$ $m^2 + 7m - 21 + 21 = -10$ Combine like terms: $\newline$ $m^2 + 7m = -10$ To get the equation in standard form, we add $10$ to both sides of the equation: $\newline$ $m^2 + 7m + 10 = 0$