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damaskus [11]
3 years ago
9

Solve for x. Enter the solutions from least to greatest. (x+15)^2-10=0

Mathematics
1 answer:
Sergeu [11.5K]3 years ago
7 0

Answer:

  • lesser x = -1.84
  • lesser x = -8.16

Step-by-step explanation:

Given the expression

\left(x+5\right)^2-10=0

Add 10 to both sides

\left(x+5\right)^2-10+10=0+10

Simplify

\left(x+5\right)^2=10

\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}

solve

x+5=\sqrt{10}

Subtract 5 from both sides

x+5-5=\sqrt{10}-5

x=\sqrt{10}-5

x=-1.8

so

x+5=-\sqrt{10}

Subtract 5 from both sides

x+5-5=-\sqrt{10}-5

Simplify

x=-\sqrt{10}-5

\:x=-8.2

As -1.84 > -8.16

so

  • lesser x = -1.84
  • lesser x = -8.16
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Find a polynomial, which, when added to the polynomial 5x2–3x–9, is equivalent to: x2−5x+6
Bess [88]

The required polynomial is:-4x^2-2x+15

Step-by-step explanation:

Let P be the polynomial that has to be found

Given

One polynomial = 5x^2-3x-9

Sum of both polynomials = x^2-5x+6

So,

(5x^2-3x-9) + P = x^2-5x+6\\P = x^2-5x+6 - (5x^2-3x-9)\\P = x^2-5x+6-5x^2+3x+9\\P = x^2-5x^2-5x+3x+6+9\\P = -4x^2-2x+15

Hence,

The required polynomial is:-4x^2-2x+15

Keywords: Polynomials, expressions

Learn more about polynomials at:

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  • brainly.com/question/1695461

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3 0
3 years ago
Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. Tha
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Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

a = 20 --- tree distance from north gate

b =14 --- movement from south gate

c = 1775 --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

\triangle ADE \sim \triangle ACB --- similar triangles

So, we have the following equivalent ratios

AE:DE = AB:CB

Where:

AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775

Substitute these in the above equation

20:x/2 = 20 + x + 14: 1775

20:x/2 = x + 34: 1775

Express as fraction

\frac{20}{x/2} = \frac{x + 34}{1775}

\frac{40}{x} = \frac{x + 34}{1775}

Cross multiply

x *(x + 34) = 1775 * 40

Open bracket

x^2 + 34x = 71000

Rewrite as:

x^2 + 34x - 71000 = 0

Expand

x^2 + 284x -250x - 71000 = 0

Factorize

x(x + 284) -250(x + 284)= 0

Factor out x + 284

(x - 250)(x + 284)= 0

Split

x - 250 = 0 \ or\ x + 284= 0

Solve for x

x = 250 \ or\ x =- 284

x can't be negative;

So:

x = 250

6 0
3 years ago
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