"To solve: The equation x2−1.800x+0.810=0 using quadratic formula..." was answered by our experts

Tabansi

Answered question

2021-05-11

To solve:
The equation

x^{2} - 1.800 x + 0.810 = 0

using quadratic formula and a calculator, rounding to three decimals.

SkladanH

Skilled2021-05-12Added 80 answers

Step 1
Quadratic Formula: For a quadratic equation

a x^{2} + b x + c = 0

, where

a \neq 0,

the solutions are

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Step 2
Given:

x^{2} - 1.800 x + 0.810 = 0

Here,

a = 1, b = - 1.800

and

c = 0.810

Substitute these values in quadratic formula.

x = \frac{- (- 1.800) \pm \sqrt{(- 1.800)^{2} - 4 (1) (0.810)}}{2 (1)}

= \frac{1.800 \pm \sqrt{3.24 - 3.24}}{2}

= \frac{1.800 \pm \sqrt{0}}{2}

Since the discriminant is 0, the equation has one real solution.

x = \frac{1.800}{2} = 0.900

Therefore, the solution of the equation is

x = 0.900

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