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

Use the Quadratic Formula to solve the quadratic below.\newlinex2−5x+9=0x^{2}-5 x+9=0

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Full solution

Q. Use the Quadratic Formula to solve the quadratic below.\newlinex2−5x+9=0x^{2}-5 x+9=0
  1. Write Quadratic Formula: Write down the quadratic formula.\newlineThe quadratic formula is used to find the solutions to a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. The formula is:\newlinex=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
  2. Identify Coefficients: Identify the coefficients aa, bb, and cc from the quadratic equation x2−5x+9=0x^2 - 5x + 9 = 0.\newlineIn this equation, a=1a = 1, b=−5b = -5, and c=9c = 9.
  3. Substitute into Formula: Substitute the coefficients into the quadratic formula. x=−(−5)±(−5)2−4(1)(9)2(1)x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(9)}}{2(1)}
  4. Simplify Equation: Simplify the equation.\newlinex=5±25−362x = \frac{5 \pm \sqrt{25 - 36}}{2}\newlinex=5±−112x = \frac{5 \pm \sqrt{-11}}{2}
  5. Complex Number Solutions: Since the discriminant (the value under the square root) is negative, the solutions will be complex numbers.\newlinex=5±−112x = \frac{5 \pm \sqrt{-11}}{2}\newlinex=5±i112x = \frac{5 \pm i\sqrt{11}}{2}
  6. Write Final Solutions: Write the final solutions.\newlineThe solutions to the quadratic equation x2−5x+9=0x^2 - 5x + 9 = 0 are:\newlinex=5+i112x = \frac{5 + i\sqrt{11}}{2} and x=5−i112x = \frac{5 - i\sqrt{11}}{2}

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