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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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.