How do you solve $5 x^{2} - 7 x - 6 = 0$ $5x^2 - 7x - 6 = 0$ by factoring?

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How do you solve $5 x^{2} - 7 x - 6 = 0$ $5x^2 - 7x - 6 = 0$ by factoring?

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Answer 1 · 2015-08-12T06:22:58

The solutions are

$x = - \frac{3}{5}$ $color(blue)(x=-3/5$
$x = 2$ $color(blue)(x=2$

Explanation:

$5 x^{2} - 7 x - 6 = 0$ $5x^2−7x−6=0$

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:

$N_{1} \cdot N_{2} = a \cdot c = 5 \cdot - 6 = - 30$ $N_1*N_2 = a*c = 5*-6 = -30$
and
$N_{1} + N_{2} = b = - 7$ $N_1 +N_2 = b = -7$

After trying out a few numbers we get $N_{1} = - 10$ $N_1 = -10$ and $N_{2} = 3$ $N_2 =3$
$- 10 \cdot 3 = - 30$ $-10*3 = -30$ , and $3 + (- 10) = - 7$ $3+(-10)= -7$

$5 x^{2} - 7 x - 6 = 5 x^{2} - 10 x + 3 x - 6$ $5x^2−color(blue)(7x)−6= 5x^2−color(blue)(10x +3x)−6$

$= 5 x (x - 2) + 3 (x - 2)$ $= 5x(x-2) + 3(x-2)$

$(5 x + 3) (x - 2)$ $color(blue)((5x+3)(x-2)$ are the factors of the expression.

Now we equate these factors to zero and find the solutions:

$5 x + 3 = 0, x = - \frac{3}{5}$ $5x+3 = 0 , color(blue)(x=-3/5$
$x - 2 = 0, x = 2$ $x-2 =0, color(blue)(x=2$

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How do you solve $5 x^{2} - 7 x - 6 = 0$ $5x^2 - 7x - 6 = 0$ by factoring?

1 Answer

Explanation:

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How do you solve 5x2−7x−6=05x^2 - 7x - 6 = 0 by factoring?

1 Answer

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How do you solve $5 x^{2} - 7 x - 6 = 0$ $5x^2 - 7x - 6 = 0$ by factoring?