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3 years ago

6

Which is a solution to the equation? (x-2)(x=5)=18

2 answers:

4vir4ik [10]3 years ago

8 0

I hope this helps you

kobusy [5.1K]3 years ago

6 0

Expand
x^2+3x-10=18
minus 18 both sides
x^2+3x-28=0
find what 2 numbers mutiply to -28 and add to 3
7 and -3
(x+7)(x-3)=0
set each to zero

x+7=0
x=-7
x-3=0
x=3

x=-7 and 3

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Solve (x + 1)2 – 4(x + 1) + 2 = 0 using substitution.

solniwko [45]

For this case we have to:

Let $u = x + 1$

So:

$u ^ 2-4u + 2 = 0$

We have the solution will be given by:

$u = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}$

Where:

$a = 1\\b = -4\\c = 2$

Substituting:

$u = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (1) (2)}} {2 (1)}\\u = \frac {4 \pm \sqrt {16-8}} {2}\\u = \frac {4 \pm \sqrt {8}} {2}\\u = \frac {4 \pm \sqrt {2 ^ 2 * 2}} {2}\\u = \frac {4 \pm2 \sqrt {2}} {2}$

The solutions are:

$u_ {1} = \frac {4 + 2 \sqrt {2}} {2} = 2 + \sqrt {2}\\u_ {2} = \frac {4-2 \sqrt {2}} {2} = 2- \sqrt {2}$

Returning the change:

$2+ \sqrt {2} = x_ {1} +1\\x_ {1} = 1 + \sqrt {2}\\2- \sqrt {2} = x_ {2} +1\\x_ {2} = 1- \sqrt {2}$

Answer:

$x_ {1} = 1 + \sqrt {2}\\x_ {2} = 1- \sqrt {2}$

3 0

3 years ago

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Given: sin(18m-12)=cos(7m+2), find the value of m.

V125BC [204]

Answer:

m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or m = 2/3 - (π n_2)/18 for n_2 element Z

Step-by-step explanation:

Solve for m:

-cos(7 m + 2) sin(12 - 18 m) = 0

Multiply both sides by -1:

cos(7 m + 2) sin(12 - 18 m) = 0

Split into two equations:

cos(7 m + 2) = 0 or sin(12 - 18 m) = 0

Take the inverse cosine of both sides:

7 m + 2 = π n_1 + π/2 for n_1 element Z

or sin(12 - 18 m) = 0

Subtract 2 from both sides:

7 m = -2 + π/2 + π n_1 for n_1 element Z

or sin(12 - 18 m) = 0

Divide both sides by 7:

m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or sin(12 - 18 m) = 0

Take the inverse sine of both sides:

m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or 12 - 18 m = π n_2 for n_2 element Z

Subtract 12 from both sides:

m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or -18 m = π n_2 - 12 for n_2 element Z

Divide both sides by -18:

Answer: m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or m = 2/3 - (π n_2)/18 for n_2 element Z

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