Solve the equation by factoring 2x^2+7x=4
2 answers:
Answer:
x = - 4 , x =
Step-by-step explanation:
given 2x² + 7x = 4
rearrange into standard form : ax² + bx + c = 0 : a ≠ 0
subtract 4 from both sides
2x² + 7x - 4 = 0 ← in standard form
Consider the product of the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term, that is
product = 2 × - 4 = - 8 and sum = + 7
The factors are + 8 and - 1
use these factors to split the middle term
2x² + 8x - x - 4 = 0 ( factor by grouping first/second and third/fourth terms )
2x(x + 4) - 1(x + 4) = 0 ( take out the common factor (x + 4) )
(x + 4)(2x - 1) = 0
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
2x - 1 = 0 ⇒ 2x = 1 ⇒ x =
You might be interested in
Answer:
Step-by-step explanation:
These problems are based on triangle ratios. You cannot use the Pythagorean theorem to solve them.
The first triangle is a 45 45 90 degree triangle (I'm talking about the angles), and so, the ratio is 1:1:, so I have to divide the hypotenuse by
to get the legs. The hypotenuse is 15
, so that divided by
is 15
. X is the same length as y because of the triangle ratio, so both x and y for the first triangle are 15
.
The second triangle is a 30 60 90 degree triangle, so the ratio is x:x:2x. The short leg is 7
, so 7
* 2 is the hypotenuse, which is 14
. The long leg is 7
*
, which is 21. So, x for the second triangle is 14
, and y for the second triangle is 21.