Solve: x² − $5x + 6 = 0$ vdhsjv

Answer: $x = 2$ or $x = 3$

Step-by-step solution

Step 1: Identify coefficients and split the middle term

We compare the given equation with the standard quadratic form $a x^2 + b x + c = 0$ , where $a = 1$ , $b = -5$ , and $c = 6$ . We need two numbers whose product is $a \times c = 6$ and whose sum is $b = -5$ . The two numbers are $-2$ and $-3$ , so we split $-5x$ into $-2x - 3x$ .

Step 2: Factor by grouping

We group the terms in pairs: $(x^2 - 2x) - (3x - 6) = 0$ . Factoring out common factors gives $x(x - 2) - 3(x - 2) = 0$ . Since $(x - 2)$ is common to both terms, we factor it out to obtain $(x - 2)(x - 3) = 0$ .

Step 3: Solve for x using the zero-product property

By the zero-product property, if the product of two factors is 0, at least one of the factors must be 0. Setting $x - 2 = 0$ gives $x = 2$ , and setting $x - 3 = 0$ gives $x = 3$ .

Solve your own maths question free →

Solve: x² − 5x+6=05x + 6 = 05x+6=0 vdhsjv

Step-by-step solution

Step 1: Identify coefficients and split the middle term

Step 2: Factor by grouping

Step 3: Solve for x using the zero-product property

Solve: x² − $5x + 6 = 0$ vdhsjv