Get the answer to "How do you solve −20x2−20x+40=0?"

Jamya Elliott

Answered question

2022-01-21

How do you solve

- 20 x^{2} - 20 x + 40 = 0

stamptsk

Beginner2022-01-22Added 23 answers

Step 1
You may start by dividing everything by 20
It also helps if you reverse all the signs.

\to - x^{2} - x + 2 = 0

\to x^{2} + x - 2 = 0

This can be factorised:

\to (x - 1) \times (x + 2) = 0

\to x = 1

x = - 2

jojoann325

Beginner2022-01-23Added 10 answers

Step 1
Again, you can use the Quadratic Formula but we can also try something interesting!
Divide all by 20;

- x^{2} - x + 2 = 0

Rearrange:

- x^{2} - x = - 2

again

x^{2} + x = 2

add and subtract

\frac{1}{4}

x^{2} + x + \frac{1}{4} - \frac{1}{4} = 2

rearrange:

x^{2} + x + \frac{1}{4} = 2 + \frac{1}{4}

{(x + \frac{1}{2})}^{2} = \frac{9}{4}

root square both sides:

x + \frac{1}{2} = \pm \sqrt{\frac{9}{4}} = \pm \frac{3}{2}

so you get two solutions:

x_{1} = - \frac{1}{2} + \frac{3}{2} = 1

x_{2} = - \frac{1}{2} - \frac{3}{2} = - 2

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