Using quadratic formula 2x2-2x+2=0

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Step 1: Identify the coefficients a, b, and c from the given quadratic equation 2x² − 2x + 2 = 0. a = 2; b = −2; c = 2 Step 2: Write down the quadratic formula. x = (−b ± √(b² − 4ac))/(2a) Step 3: Substitute the values of a, b, and c into the quadratic formula. x = (−(−2) ± √((−2)² − 4(2)(2)))/(2(2)) Step 4: Simplify the expression. x = (2 ± √(4 − 16))/(4); x = (2 ± √(−12))/(4); Step 5: Simplify the square root of the negative number. Recall that √(−1) = i. x = (2 ± √(12)i)/(4); x = (2 ± √(4 × 3)i)/(4); x = (2 ± 2√(3)i)/(4) Step 6: Divide all terms by the common factor of 2. x = (2(1 ± √(3)i))/(4); x = (1 ± √(3)i)/(2) The solutions are: x₁ = (1 + √(3)i)/(2); x₂ = (1 − √(3)i)/(2); The final answers are x = (1 ± √(3)i)/(2).

Using quadratic formula 2x2−2x+2=0

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Step-by-step solution

Identify the coefficients $a$ , $b$ , and $c$ from the given quadratic equation $2x^2 - 2x + 2 = 0$ .

Write down the quadratic formula.

Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula.

Simplify the expression.

Simplify the square root of the negative number.

Divide all terms by the common factor of 2.

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