Algebra Examples

$0 = x^{2} - 4 x + 10$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $x^{2}$ from both sides of the equation.

$- x^{2} = - 4 x + 10$

Step 1.2

Add $4 x$ to both sides of the equation.

$- x^{2} + 4 x = 10$

Step 1.3

Subtract $10$ from both sides of the equation.

$- x^{2} + 4 x - 10 = 0$

Step 2

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 3

Substitute in the values of $a$ , $b$ , and $c$ .

$4^{2} - 4 (- - 10)$

Step 4

Evaluate the result to find the discriminant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Raise $4$ to the power of $2$ .

$16 - 4 (- - 10)$

Step 4.1.2

Multiply $- 4 (- - 10)$ .

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Step 4.1.2.1

Multiply $- 1$ by $- 10$ .

$16 - 4 \cdot 10$

Step 4.1.2.2

Multiply $- 4$ by $10$ .

$16 - 40$

Step 4.2

Subtract $40$ from $16$ .

$- 24$