Respuesta :
Answer:
x = 1 ± 2i
Step-by-step explanation:
x² - 2x + 5 = 0 ( add 5 to both sides )
x² - 2x = - 5
Using the method of completing the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(- 1)x + 1 = - 5 + 1
(x - 1)² = - 4 ( take square root of both sides )
x - 1 = ± [tex]\sqrt{-4}[/tex] = ± 2i ( add 1 to both sides )
x = 1 ± 2i ( that is the solutions are complex )
Answer:
[tex]x=1\pm2i[/tex]
or
[tex]x=1+2i[/tex]
[tex]x=1-2i[/tex]
Step-by-step explanation:
All equations of the form [tex]ax^2+bx+c=0[/tex] can be solved using the quadratic formula: [tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
Quadratic formula gives two solutions, one when ± is addition add one when it is subtraction.
[tex]x^2-2x+5=0[/tex]
Equation is in standard form: [tex]ax^2+bx+c=0[/tex]
Substitute 1 from a, [tex]-2[/tex] for b, and [tex]5[/tex] for C in the quadratic formula, [tex]\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\times \:1\times \:5}}{2}[/tex]
Multiply -4 × 5:
[tex]x=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \:5}}{2}[/tex]
Add 4 + -20:
[tex]x=\frac{-\left(-2\right)\pm \:4i}{2}[/tex]
* the opposite of -2 is 2:
[tex]x=\frac{2\pm 4i}{2}[/tex]
Now, solve equation:
[tex]x=\frac{2+4i}{2}[/tex]
Divide 2 + 4i by 2:
[tex]x=1-2i[/tex]
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