How do you solve $4 x^{2} + 4 x - 3 = 0$ $4x^2 + 4x - 3 = 0$ by factoring?

Question

How do you solve $4 x^{2} + 4 x - 3 = 0$ $4x^2 + 4x - 3 = 0$ by factoring?

1 Answer

Impact of this question

13893 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-12T06:36:48

The solutions for the equation are
$x = - \frac{3}{2}, x = \frac{1}{2}$ $color(blue)(x=-3/2, x=1/2$

Explanation:

$4 x^{2} + 4 x - 3$ $4x^2+4x−3$

We can Split the Middle Term of this expression to factorise it and thereby find the solutions.

In this technique, if we have to factorise an expression like $a x^{2} + b x + c$ $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 4 \cdot (- 3) = - 12$ $N_1*N_2 = a*c = 4*(-3) = -12$
and
$N_{1} + N_{2} = b = 4$ $N_1 +N_2 = b = 4$

After trying out a few numbers we get $N_{1} = 6$ $N_1 = 6$ and $N_{2} = - 2$ $N_2 =-2$
$6 \cdot (- 2) = - 12$ $6*(-2) = -12$ , and $6 + (- 2) = 4$ $6+(-2)= 4$

$4 x^{2} + 4 x - 3 = 4 x^{2} - 2 x + 6 x - 3$ $4x^2+color(blue)(4x)−3 =4x^2-color(blue)(2x +6x)−3$

$= 2 x (2 x - 1) + 3 (2 x - 1)$ $=2x(2x-1) +3(2x-1)$

$(2 x + 3) (2 x - 1)$ $color(blue)((2x+3)(2x-1)$ is the factorised form of the expression.

Now we can equate each of the two factors to zero and find the solutions.

$2 x + 3 = 0, x = - \frac{3}{2}$ $2x+3 = 0, color(blue)(x=-3/2$
$2 x - 1 = 0, x = \frac{1}{2}$ $2x-1=0, color(blue)(x=1/2$

Science

Math

Humanities

... and beyond

How do you solve $4 x^{2} + 4 x - 3 = 0$ $4x^2 + 4x - 3 = 0$ by factoring?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve 4x2+4x−3=04x^2 + 4x - 3 = 0 by factoring?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve $4 x^{2} + 4 x - 3 = 0$ $4x^2 + 4x - 3 = 0$ by factoring?