Question

What is the solutions of the quadratic equation?

x2 = 9x + 6

Answer 1

The solutions to the quadratic equation x2 = 9x + 6 can be found by rearranging it to x2 - 9x - 6 = 0 and using the quadratic formula, resulting in two possible solutions.

Step-by-step explanation:

The solutions of the quadratic equation x2 = 9x + 6 can be found by rearranging the equation into the standard form ax2 + bx + c = 0 and then applying the quadratic formula. First, we subtract 9x and 6 from both sides to get 0 on one side, resulting in x2 - 9x - 6 = 0. Now we can use the quadratic formula to solve for x:

For a quadratic equation of the form ax2 + bx + c = 0, the quadratic formula is x = (-b ± √(b2 - 4ac)) / (2a). Plugging in the values a = 1, b = -9, and c = -6 into the formula gives us:

x = (9 ± √((9)2 - 4(1)(-6))) / (2(1))

x = (9 ± √(81 + 24)) / 2

x = (9 ± √105) / 2

Finally, solving the equation gives us two potential solutions, which are the roots of the quadratic equation.

Answer 2

hello :
note :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x = (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions
in this exercice :
x² = 9x+6
x² -9x -6 = 0
Δ = b² - 4ac ... a =1 b = -9 c =-6
Δ = (-9)² -4(1)(-6)=105..........
He continued...