Solve x^2-2x+5 = 0

Solve ax² + bx + c = 0 using the quadratic formula with discriminant analysis.

Equation

Answer

x = 1 ± 2i

x²-2x+5=0

Solve using the quadratic formula since this quadratic does not factor nicely:

Step 1 — Identify the coefficients

Compare with the standard form ax² + bx + c = 0:

a = 1, b = −2, c = 5

Step 2 — Substitute into the quadratic formula

x = (−b ± √b² − 4ac) / 2a

x = (2 ± √(-2)² − 4(1)(5)) / 2(1)

x = (2 ± √4 − 20) / 2

x = (2 ± √-16) / 2

Step 3 — Evaluate the discriminant

Δ = b² − 4ac = 4 − 20 = -16

Since Δ = -16 is negative, the solutions are complex:

x = 1 ± 2i

How to solve x^2-2x+5 = 0

To solve x^2-2x+5 = 0, we can try factoring, use the quadratic formula, or complete the square. The solution is x = 1 ± 2i.

This is a second-degree quadratic equation — the highest power of the variable is 2. Quadratic equations can have two real roots, one repeated root, or two complex roots.

Frequently asked questions

What is the answer to x^2-2x+5 = 0?
The answer is x = 1 ± 2i.

What method is used?
factoring when possible, or the quadratic formula x = (−b ± √(b²−4ac)) / 2a. The discriminant b²−4ac determines the number and type of solutions.

How do I verify this?
Substituting the solution(s) back into x^2-2x+5 = 0 confirms both sides are equal.

More quadratic formula calculator problems

x² + 5x + 6 = 0 x² − 4 = 0 2x² − 3x − 2 = 0 x² + 2x − 8 = 0 x² − 6x + 9 = 0 3x² + x − 2 = 0 x² − 9 = 0 x² + 4x + 4 = 0 x² − x − 12 = 0 4x² − 1 = 0 x² + 3x = 10 2x² = 18