Use the Quadratic Formula to solve the quadratic below: x^(2)-5x+9=0

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Use the Quadratic Formula to solve the quadratic below:  x^(2)-5x+9=0

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Identify coefficients: Identify the coefficients a, b, and c in the quadratic equation x^2 - 5x + 9 = 0. By comparing x^2 - 5x + 9 with the standard quadratic form ax^2 + bx + c, we find that a = 1, b = -5, and c = 9.Apply Quadratic Formula: Apply the Quadratic Formula to find the roots of the equation. The Quadratic Formula is given by (-b ± √(b^2 - 4ac)) / (2a). We will substitute a = 1, b = -5, and c = 9 into the formula.Substitute values: Substitute the values of a, b, and c into the Quadratic Formula. (-(-5) ± √((-5)^2 - 4*1*9)) / (2*1) simplifies to (5 ± √(25 - 36)) / 2.Simplify square root: Simplify the expression under the square root. 25 - 36 = -11, so the expression becomes (5 ± √(-11)) / 2.Complex roots: Since the value under the square root is negative, we will have complex roots. We can express √(-11) as √(11) * √(-1), where √(-1) is the imaginary unit i. The expression becomes (5 ± √(11)i) / 2.Divide by 2: Simplify the expression by dividing both terms by 2. (5/2) ± (√(11)/2)i is the simplified form of the roots in a+bi form.Write in a+bi form: Write the roots in the simplest a+bi form. The roots are 5/2 + (√(11)/2)i and 5/2 - (√(11)/2)i.

Use the Quadratic Formula to solve the quadratic below: $\newline$ $x^{2}-5x+9=0$

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Use the Quadratic Formula to solve the quadratic below: $\newline$ $x^{2}-5x+9=0$