# What are two numbers which multiply to make -9450 and add to make -15 ?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

1
Nimo N. Share
Jun 6, 2018

The question was changed after posting my original answer... I re-worked the problem and obtained two possible combinations.

#### Explanation:

"two numbers add to make -15" gives equation 1):
1) $A + B = - 15$
"two numbers multiply to make -9450", gives:
2) $A B = - 9450$

Solve equation 1) for A, then substitute into equation 2), to get B.
1a) $A = - 15 - B$
$\left(- 15 - B\right) B = - 9450$
Multiply, then add 9450 to both sides, to get,
$- 15 B - {B}^{2} + 9450 = 0$
$- {B}^{2} - 15 B + 9450 = 0$
$B = \frac{- \left(- 15\right) \pm \sqrt{{\left(- 15\right)}^{2} - 4 \left(- 1\right) \left(9450\right)}}{2 \left(- 1\right)}$
$B = \frac{15 \pm \sqrt{225 + 37800}}{- 2}$

$B = \frac{15 \pm \sqrt{38025}}{- 2}$

${B}_{\text{using} -} = \frac{15 - \sqrt{38025}}{- 2}$
${B}_{\text{using} -} = 90$
$- - - - -$

${B}_{\text{using} +} = \frac{15 + \sqrt{37825}}{- 2}$
${B}_{\text{using} +} = \frac{- 15 - 5 \sqrt{1513}}{2}$, Exact.
${B}_{\text{using} +} = - 104.74$, Approximate.
$- - - - -$

Substitute into 1a) to obtain two possible (approximate) values for A.
$A = - 15 - \left(90\right)$
$A = - 105$

$A = - 15 - \left(- 104.74\right)$
$A = 89.74$

There are two possible combinations of numbers for A and B:
( -105, 90)
(89.74, -104.74 )

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

1
Jun 6, 2018

$- 105 \times 90 = - 9450$

$- 105 + 90 = - 15$

#### Explanation:

One number has to be positive and one has to be negative to give a negative product.

Factors which differ by $15$ are close to the square root of a number. They will be about $7$ bigger or smaller than the square root.

$\sqrt{9450} = 97.211 \ldots$

Try numbers less than $97$

$9450 \div 95 = 99.47 \text{ } \leftarrow$ does not work
$9450 \div 94 = 100.53 \text{ } \leftarrow$ does not work
$9450 \div 90 = 105 \text{ } \leftarrow$ These are the factors

$- 105 \times 90 = - 9450$

$- 105 + 90 = - 15$

• 12 minutes ago
• 13 minutes ago
• 14 minutes ago
• 16 minutes ago
• 4 seconds ago
• A minute ago
• A minute ago
• 4 minutes ago
• 5 minutes ago
• 8 minutes ago
• 12 minutes ago
• 13 minutes ago
• 14 minutes ago
• 16 minutes ago