Respuesta :

Answer:

[tex]x=\dfrac{1}{8}, \quad x=-2[/tex]

Step-by-step explanation:

Given equation:

[tex](8x+7)(x+1)=9[/tex]

Expand the brackets:

[tex]\implies 8x^2+15x+7=9[/tex]

Subtract 9 from both sides:

[tex]\implies 8x^2+15x+7-9=9-9[/tex]

Simplify:

[tex]\implies 8x^2+15x-2=0[/tex]

To factor a quadratic equation in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]\implies ac=8 \cdot -2=-16[/tex]

[tex]\implies b=15[/tex]

Therefore, the two numbers are:  16 and -1.

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies 8x^2+16x-x-2=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 8x(x+2)-1(x+2)=0[/tex]

Factor out the common term (x + 2):

[tex]\implies (8x-1)(x+2)=0[/tex]

Apply the zero-product property:

[tex]\implies 8x-1=0 \implies x=\dfrac{1}{8}[/tex]

[tex]\implies x+2=0 \implies x=-2[/tex]

Therefore, the solutions to the given quadratic equation are:

[tex]x=\dfrac{1}{8}, \quad x=-2[/tex]

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ItzTds

Answer:

x = 1/8 (or) x = -2

Step-by-step explanation:

Now we have to,

→ solve the following quadratic equation.

Let's solve for quadratic equation,

→ (8x+7)(x+1) = 9

→ 8x² + 7x + 8x + 7 - 9

→ 8x² + 15x - 2

→ 8x² + 16x - x - 2

→ 8x(x + 2) - 1(x + 2)

→ (8x - 1)(x + 2)

→ x = 1/8 (or) x = -2

Hence, the solution is x = 1/8, -2.