Question

Solve for x :(x+4) (x+5)=3(x+1)(x+2)+2x

Answer 1

hello
factorise the ladt part and u can get the value
for x

Answer 2

Answer:

$x=\frac{-1}{2} +\frac{1}{2}\sqrt{29}\\x=\frac{-1}{2} -\frac{1}{2}\sqrt{29}$

Step-by-step explanation:

Given:

(x+4) (x+5)=3(x+1)(x+2)+2x

To find:

The value x.

Solution:

A polynomial equation is said to be quadratic if the maximum power associated with a variable is of order 2. Given that the polynomial equation's maximum power is 2, it follows that the equation must contain at least one component that is squared. As a result, the equation is referred to as a "quad."

The general form of a quadratic equation is a$x^{2}$+bx+c=0, where a, b, and c are numerical coefficients or constants and x is a variable number. The initial constant's value can never be 0, which is one of the basic principles of a quadratic equation.

These equations make up a sizeable portion of what is required to resolve many sorts of challenging mathematical puzzles.

$(x+4) (x+5)=3(x+1)(x+2)+2xx^{2} +5x+4x+20=3[x^{2}+2x+x+2]+2xx^{2} +9x+20=3x^{2} +9x+6+2x\\x^{2} +9x+20=3x^{2} +11x+6\\-2x^{2} -2x+14=0$

Now using the quadratic formula with

a=-2, b=-2, c=14

$x=\frac{-b±\sqrt{b^{2}-4sc }}{2a} \\x=\frac{2±\sqrt{116} }{-4} \\x=\frac{-1}{2} +\frac{-1}{2} \sqrt{29}$

or

$x=\frac{-1}{2} +\frac{1}{2}\sqrt{29}$

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