Solved on Jan 27, 2024

Find the values of $m$ that satisfy the quadratic equation $m^{2} + m - 90 = 0$ .

STEP 1

Assumptions
1. We are given a quadratic expression $m^{2} + m - 90$ .
2. The task is to solve the quadratic expression, which typically means factoring it into the product of two binomials if possible.

STEP 2

To factor the quadratic expression, we look for two numbers that multiply to the constant term (-90) and add up to the coefficient of the linear term (1).

STEP 3

List the pairs of factors of -90, considering both positive and negative values because the product needs to be negative:
\begin{align} (1, -90) \\ (-1, 90) \\ (2, -45) \\ (-2, 45) \\ (3, -30) \\ (-3, 30) \\ (5, -18) \\ (-5, 18) \\ (6, -15) \\ (-6, 15) \\ (9, -10) \\ (-9, 10) \\ \end{align}

STEP 4

From the list of factor pairs, identify the pair that adds up to 1 (the coefficient of the linear term $m$ ).
$9 + (-10) = -1$
This is close, but we need a positive 1, so we need to reverse the signs:
$-9 + 10 = 1$

STEP 5

Now that we have identified the correct pair of numbers, we can write the quadratic expression as the product of two binomials using these numbers.
$m^{2} + m - 90 = (m - 9)(m + 10)$

STEP 6

The quadratic expression $m^{2} + m - 90$ is now factored as $(m - 9)(m + 10)$ .

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Find the values of $m$ that satisfy the quadratic equation $m^{2} + m - 90 = 0$ .

STEP 1

Assumptions
1. We are given a quadratic expression $m^{2} + m - 90$ .
2. The task is to solve the quadratic expression, which typically means factoring it into the product of two binomials if possible.

STEP 2

To factor the quadratic expression, we look for two numbers that multiply to the constant term (-90) and add up to the coefficient of the linear term (1).

STEP 3

List the pairs of factors of -90, considering both positive and negative values because the product needs to be negative:
\begin{align} (1, -90) \\ (-1, 90) \\ (2, -45) \\ (-2, 45) \\ (3, -30) \\ (-3, 30) \\ (5, -18) \\ (-5, 18) \\ (6, -15) \\ (-6, 15) \\ (9, -10) \\ (-9, 10) \\ \end{align}

STEP 4

From the list of factor pairs, identify the pair that adds up to 1 (the coefficient of the linear term $m$ ).
$9 + (-10) = -1$
This is close, but we need a positive 1, so we need to reverse the signs:
$-9 + 10 = 1$

STEP 5

Now that we have identified the correct pair of numbers, we can write the quadratic expression as the product of two binomials using these numbers.
$m^{2} + m - 90 = (m - 9)(m + 10)$

STEP 6

The quadratic expression $m^{2} + m - 90$ is now factored as $(m - 9)(m + 10)$ .

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Find the values of mmm that satisfy the quadratic equation m2+m−90=0m^{2} + m - 90 = 0m2+m−90=0.

STEP 1

Assumptions1. We are given a quadratic expression m2+m−90 m^{2} + m - 90 m2+m−90.2. The task is to solve the quadratic expression, which typically means factoring it into the product of two binomials if possible.

STEP 2

To factor the quadratic expression, we look for two numbers that multiply to the constant term (-90) and add up to the coefficient of the linear term (1).

STEP 3

List the pairs of factors of -90, considering both positive and negative values because the product needs to be negative:\begin{align*} (1, -90) \\ (-1, 90) \\ (2, -45) \\ (-2, 45) \\ (3, -30) \\ (-3, 30) \\ (5, -18) \\ (-5, 18) \\ (6, -15) \\ (-6, 15) \\ (9, -10) \\ (-9, 10) \\ \end{align*}

STEP 4

From the list of factor pairs, identify the pair that adds up to 1 (the coefficient of the linear term m m m).9+(−10)=−19 + (-10) = -19+(−10)=−1This is close, but we need a positive 1, so we need to reverse the signs:−9+10=1-9 + 10 = 1−9+10=1

STEP 5

Now that we have identified the correct pair of numbers, we can write the quadratic expression as the product of two binomials using these numbers.m2+m−90=(m−9)(m+10)m^{2} + m - 90 = (m - 9)(m + 10)m2+m−90=(m−9)(m+10)

STEP 6

The quadratic expression m2+m−90 m^{2} + m - 90 m2+m−90 is now factored as (m−9)(m+10) (m - 9)(m + 10) (m−9)(m+10).

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the values of $m$ that satisfy the quadratic equation $m^{2} + m - 90 = 0$ .

Assumptions
1. We are given a quadratic expression $m^{2} + m - 90$ .
2. The task is to solve the quadratic expression, which typically means factoring it into the product of two binomials if possible.

List the pairs of factors of -90, considering both positive and negative values because the product needs to be negative:
\begin{align} (1, -90) \\ (-1, 90) \\ (2, -45) \\ (-2, 45) \\ (3, -30) \\ (-3, 30) \\ (5, -18) \\ (-5, 18) \\ (6, -15) \\ (-6, 15) \\ (9, -10) \\ (-9, 10) \\ \end{align}

From the list of factor pairs, identify the pair that adds up to 1 (the coefficient of the linear term $m$ ).
$9 + (-10) = -1$
This is close, but we need a positive 1, so we need to reverse the signs:
$-9 + 10 = 1$

Now that we have identified the correct pair of numbers, we can write the quadratic expression as the product of two binomials using these numbers.
$m^{2} + m - 90 = (m - 9)(m + 10)$

The quadratic expression $m^{2} + m - 90$ is now factored as $(m - 9)(m + 10)$ .