Question

Solve by factoring or finding square roots. -4x^2+3x = -1

Answer 1

x = -1/4 or x= 1

Explanation:

Given equation is:

-4x²+3x+1 = 0

Make above equation in the form where a = 1.

Dividing by -4 to both sides of above equation , we have

-4x²/-4+3x/-4 = -1/-4

x²-3/4x = 1/4

x²-3/4x-1/4 = 0

Split the middle term of above equation so that the sum of two terms should be -3/4 and product is -1/4.

x²+1/4x-x-1/4 = 0

Making two groups

x(x+1/4)-1(x+1/4) = 0

Take (x+1/4) as common

(x+1/4)(x-1) = 0

Apply Zero-Product Property to above equation , we have

x+1/4 = 0 or x-1 = 0

x = -1/4 or x= 1

Hence , the solution is {-1/4,1}.

Answer 2

Answer:
`(x+(1)/(4))(x-1)=0\\x_1=-(1)/(4)\\x_2=1`

Explanation:

1. To solve this problem the first thing you can do is divide both sides of the quadractic equation by -4, then:

`x^(2)-(3)/(4)x+(1)/(4)=0`

2. Now, to factor the quadratic equation you must find two numbers whose sum is -3/4 and the product is 1/4. These numbers are -1/4 and 1. Therefore, you have:

`(x+(1)/(4))(x-1)=0`

3. And the roots are:

`x_1=-(1)/(4)\\x_2=1`