-4x^2=-36x+80 — step-by-step solution

⚠Ⓘ 4x is read as the product 4*x: for a power, write 4^x‖36x is read as the product 36*x: for a power, write 36^x

1) Let's solve in

ℝ

-4 x^{2} = - 36 x + 80

You can rewrite the expression as:

- ({(2 x - 9)}^{2} - 1)

- {(2 x - 9)}^{2} + 1

- {(2 x - 9)}^{2} + 1 = 0

This expression can be factorized into:

- ((2 x - 9) - 1) \cdot ((2 x - 9) + 1)

2) Let's solve in

ℝ

- ((2 x - 9) - 1) \cdot ((2 x - 9) + 1) = 0

ℹ

- 9 - 1

-10

‖

- 9 + 1

-8

- (2 x - 10) \cdot (2 x - 8)

3) Let's solve in

ℝ

- (2 x - 10) = 0

- 2 x + 10

2 x = 10

x = \frac{10}{2}

Solution found:

x = 5

4) Let's solve in

ℝ

2 x - 8 = 0

2 x = 8

x = \frac{8}{2}

Solution obtained:

x = 4

▶Solution:

x = {4, 5}