Answer :

NewStar01

[tex]\huge\ \star\;{\underline{\underline{\pmb{\mathtt{Answer:}}}}}[/tex]

To solve the equation 2x + 5 = (x + 5)², let's expand the square on the right side:

  • (x + 5)² = x² + 10x + 25

Now, let's set the equation equal to zero:

  • x² + 10x + 25 - 2x - 5 = 0

This simplifies to:

  • x² + 8x + 20 = 0

Let's use the quadratic formula to solve the equation x² + 8x + 20 = 0

The quadratic formula is:

  • [tex]\sf[x = \frac{{-b \: \pm \: \sqrt{{b^2 - 4ac}}}}{{2a}}][/tex]

In this equation, (a = 1), (b = 8), and (c = 20).

Substituting these values into the formula:

  • [tex]\sf[x = \frac{{-8 \: \pm \: \sqrt{{8^2 \: - \: 4 \times 1 \times 20}}}}{{2 \times 1}}][/tex]

  • [tex]\sf[x = \frac{{-8 \pm \sqrt{{64 - 80}}}}{{2}}][/tex]

  • [tex]\sf[x = \frac{{-8 \: \pm \: \sqrt{{-16}}}}{{2}}] [/tex]

The square root of -16 is not a real number, which means this quadratic equation has no real solutions.

  • Therefore, the original equation (2x + 5) = (x + 5)² also has no real solutions.
ag3347040

Answer:

To solve the equation 2x + 5 = (x + 5)², follow these steps:

1. Expand the right side of the equation:

(x + 5)² = (x + 5)(x + 5) = x² + 10x + 25

2. Rewrite the equation with the expanded expression:

2x + 5 = x² + 10x + 25

3. Rearrange the terms to set the equation equal to zero:

x² + 10x + 25 - 2x - 5 = 0

4. Combine like terms:

x² + 8x + 20 = 0

5. To solve for x, you can either use the quadratic formula or factor the quadratic expression. Let's use the quadratic formula:

x = [-b ± √(b² - 4ac)] / (2a)

where a = 1, b = 8, and c = 20.

6. Plug in the values of a, b, and c into the quadratic formula and solve for x:

x = [-8 ± √(8² - 4(1)(20))] / (2(1))

= [-8 ± √(64 - 80)] / 2

= [-8 ± √(-16)] / 2

Since the discriminant (b² - 4ac) is negative, the roots will be complex.

Therefore, the solutions for the equation 2x + 5 = (x + 5)² are complex numbers.