Solve the Quadratic Equation: x²-2x+8=0 Step-by-Step

Video Solution

Solution Steps

00:05 Let's find the value of X.

00:09 First, let's identify the coefficients. Pay attention to the numbers in front of the variables.

00:21 Next, we'll use the roots formula. This helps us find solutions to the equation.

00:50 Now, substitute the correct values based on the data we have, and let's solve the equation.

01:18 Let's calculate the square and the products step by step.

01:29 Remember! A root cannot be negative. Keep this in mind.

01:38 So, there's no solution to this question. Great try, and keep practicing!

Step-by-Step Solution

To solve the quadratic equation $x^2 - 2x + 8 = 0$ , we'll apply the quadratic formula method. The process is as follows:

Step 1: Identify the coefficients from the equation: $a = 1$ , $b = -2$ , $c = 8$ .
Step 2: Calculate the discriminant using the formula $\Delta = b^2 - 4ac$ .
Step 3: For the given equation, calculate $\Delta = (-2)^2 - 4(1)(8) = 4 - 32 = -28$ .
Step 4: Interpret the discriminant. Since $\Delta = -28$ is negative, this indicates there are no real solutions to the equation.

Without real roots, the equation has complex solutions. Since the problem requires real solutions, we conclude:

The equation $x^2 - 2x + 8 = 0$ has no real solution.