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

Video Solution

Solution Steps

00:00 Find X

00:04 Let's identify the coefficients

00:16 Let's use the roots formula

00:45 Let's substitute appropriate values according to the given data and solve

01:13 Let's calculate the square and products

01:24 A root cannot be a negative number

01:33 Therefore there is no solution to the question

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.