Question

Use the quadratic formula to find the exact solutions of x2 − 9x + 5 = 0.

x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a

x equals negative 9 plus or minus the square root of 101, all over 2
x equals 9 plus or minus the square root of 101, all over 2
x equals negative 9 plus or minus the square root of 61, all over 2
x equals 9 plus or minus the square root of 61, all over 2

Answer 1

The exact solution to the quadratic expression is $x=\frac{9\pm \sqrt{101}}{2}$

How to use the quadratic formula to solve the equation

Given the quadratic equation expressed as:

x^2 − 9x + 5 = 0.

From the equation, a = 1, b = -9 and c = 5

Substitute into the formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\x=\frac{9\pm \sqrt{9^2-4(5)(1)}}{2(1)}$

Simplify the given expression to have:

$x=\frac{9\pm \sqrt{101}}{2}$

Hence the exact solution to the quadratic expression is $x=\frac{9\pm \sqrt{101}}{2}$

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