50 points and brainliest fo the first correct solutions

Qn 9.

9. x =0 or x = -3/2

Step-by-step explanation:

9.  4x^2 +6x =0. The first step is to factor x;

x(4x+6) =0.

This implies that either;

x=0 or 4x+6 =0.

Solving for x yields;

4x =-6 which upon dividing both sides by 4 becomes x =-3/2.  

x =0 or x = -3/2 are the solutions to the given quadratic equation.

Qn 10.

10. x =0 or x =3

Step-by-step explanation:

10.  7x^2 =21x.

The equation can be rewritten as;

7x^2 -21x =0.

We note that 7x is a common multiple and we factor it out;

7x(x-3)=0. This implies that either;

7x =0 or x-3 =0. Solving 7x =0 yields;

x=0. Solving x-3 = 0 yields;

x =3.

x =0 or x =3 are the solutions to the given quadratic equation

Qn 11.

11. x = -9 or x = 5

Step-by-step explanation:

11.  (x+2)^2 =49.

The equation is already in factored form. The next step is to obtain square roots on both sides of the equation which yields;

(x+2) =±7. This implies that;

x = -2±7.

x = -9 or x = 5 are the solutions to the given quadratic equation.

Qn 12.

12.  x =3/8 or x = -1/3.

Step-by-step explanation:

12.  x+3 =24x^2.

The first step is to write the equation in the standard form;

24x^2 -x -3 =0.

The next step we make the coefficient of x^2 equal to 1 by diving all through by 24;

x^2 -(1/24)x - (1/8) =0.

Consequently, we determine two numbers whose sum is -(1/24) and their product -(1/8). By trial and error the two numbers are found to be; -(3/8) and (1/3). The equation is then re-written as;

x^2 +(1/3)x -(3/8)x -(1/8) =0. The equation is then factored as;

x(x +1/3) -3/8 (x +1/3) =0. Upon simplification this becomes;

(x -3/8)(x +1/3) =0. Implying that;

x =3/8 or x = -1/3 are the solutions to the given quadratic equation.

Qn 13.

13.  x =2.5 or x = -2

We plot the individual functions using the Desmos graphing utility; an online graphing tool. Consequently we determine the x-intercept which represents the zeros of the given function;

The graphical solutions to the first equation are; x =2.5 or x = -2.

Qn. 14

The graphical solutions to the this equation are; x =3.5 or x = -1.33.

Qn. 15

The graphical solutions to the this equation are; x =0.42 or x = -7.17.

Qn. 16

The graphical solutions to the this equation are; x =3.25 or x = -2.

Qn. 17

The graphical solutions to the this equation are; x =4.5 or x = -0.67.

Qn. 18

The graphical solutions to the this equation are; x =0.46 or x = -2.71.

Qn .19

19.  x^2 +x -20 =0.

Step-by-step explanation:

If 4 and -5 are the solutions to a quadratic equation, this implies;

x =4 or x = -5.

Consequently;

x -4 =0 or x +5 =0.

(x -4)(x+5) =0.

Opening the brackets and simplifying yields;

 x^2 +x -20 =0.

Qn. 20

20.  x^2 +6x  =0

Step-by-step explanation:

If -6 and 0 are the solutions to a quadratic equation, then;

x =-6 or x = 0.

This implies that;

x +6 =0 or x =0.

Consequently;

x(x+ 6) =0

Opening the brackets and simplifying yields;

 x^2 +6x  =0.

Qn. 21

21.  x^2 -11x +24 =0

Step-by-step explanation:

If 3 and 8 are the solutions to a quadratic equation, then;

x =3 or x = 8.

This implies that;

x -3 =0 or x -8 =0.

Consequently;

(x -3)(x -8) =0

Opening the brackets and simplifying yields;  

x^2 -11x +24 =0.

15

step-by-step explanation: