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

Solve the following equation:

$x^2-2x+8=0$

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.