The equation from the image is x² − 4x + 5 = 0. Step 1: Identify the coefficients of the quadratic equation ax² + bx + c = 0. From x² − 4x + 5 = 0: a = 1; b = −4; c = 5 Step 2: Apply the quadratic formula. The quadratic formula is: x = (−b ± √(b² − 4ac))/(2a) Step 3: Substitute the identified coefficients into the formula. x = (−(−4) ± √((−4)² − 4(1)(5)))/(2(1)) Step 4: Simplify the expression under the square root (the discriminant). x = (4 ± √(16 − 20))/(2); x = (4 ± √(−4))/(2); Step 5: Simplify the square root of the negative number using the imaginary unit i, where i = √(−1). √(−4) = √(4 × −1) = √(4) × √(−1) = 2i Step 6: Substitute the simplified square root back into the formula and simplify the entire expression. x = (4 ± 2i)/(2); x = (2(2 ± i))/(2); x = 2 ± i The solutions are: x₁ = 2 + i; x₂ = 2 − i The final answers are 2 ± i.

Complex numbers

October 24, 2026Mathematics

ScanSolve AI Answer

Answer

2 \pm i

Step-by-step solution

6 steps

The equation from the image is $x^2 - 4x + 5 = 0$ .

Identify the coefficients of the quadratic equation $ax^2 + bx + c = 0$ .
From $x^2 - 4x + 5 = 0$ :
$a = 1$
$b = -4$
$c = 5$
Apply the quadratic formula.
The quadratic formula is:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Substitute the identified coefficients into the formula.
$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(5)}}{2(1)}$
Simplify the expression under the square root (the discriminant).
$x = \frac{4 \pm \sqrt{16 - 20}}{2}$ $x = \frac{4 \pm \sqrt{-4}}{2}$
Simplify the square root of the negative number using the imaginary unit $i$ , where $i = \sqrt{-1}$ .
$\sqrt{-4} = \sqrt{4 \times -1} = \sqrt{4} \times \sqrt{-1} = 2i$
Substitute the simplified square root back into the formula and simplify the entire expression.
$x = \frac{4 \pm 2i}{2}$ $x = \frac{2(2 \pm i)}{2}$ $x = 2 \pm i$
The solutions are:
$x_1 = 2 + i$
$x_2 = 2 - i$

The final answers are $2 \pm i$ .

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Complex numbers

Answer

Step-by-step solution

Identify the coefficients of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0.

Apply the quadratic formula.

Substitute the identified coefficients into the formula.

Simplify the expression under the square root (the discriminant).

Simplify the square root of the negative number using the imaginary unit iii, where i=−1i = \sqrt{-1}i=−1​.

Substitute the simplified square root back into the formula and simplify the entire expression.

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More Mathematics Questions

Identify the coefficients of the quadratic equation $ax^2 + bx + c = 0$ .

Simplify the square root of the negative number using the imaginary unit $i$ , where $i = \sqrt{-1}$ .