We read your photo as:

X² + 2x + 6 = 0

Mathematics

ScanSolve AI Answer

Answer

−1±5i-1 \pm \sqrt{5}i

Step-by-step solution

6 steps

The equation from the image is x2+2x+6=0x^2 + 2x + 6 = 0.

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

    From x2+2x+6=0x^2 + 2x + 6 = 0:
    a=1a = 1
    b=2b = 2
    c=6c = 6

  2. Apply the quadratic formula.

    The quadratic formula is:

    x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

  3. Substitute the identified coefficients into the formula.

    x=−(2)±(2)2−4(1)(6)2(1)x = \frac{-(2) \pm \sqrt{(2)^2 - 4(1)(6)}}{2(1)}

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

    x=−2±4−242x = \frac{-2 \pm \sqrt{4 - 24}}{2} x=−2±−202x = \frac{-2 \pm \sqrt{-20}}{2}

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

    −20=20×−1=4×5×−1=25i\sqrt{-20} = \sqrt{20 \times -1} = \sqrt{4 \times 5} \times \sqrt{-1} = 2\sqrt{5}i

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

    x=−2±25i2x = \frac{-2 \pm 2\sqrt{5}i}{2} x=2(−1±5i)2x = \frac{2(-1 \pm \sqrt{5}i)}{2} x=−1±5ix = -1 \pm \sqrt{5}i

    The solutions are:
    x1=−1+5ix_1 = -1 + \sqrt{5}i
    x2=−1−5ix_2 = -1 - \sqrt{5}i

    The final answers are −1±5i-1 \pm \sqrt{5}i.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QSolve for x: x²+x−6=0
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp