Write a program that will solve a quadratic equation: ax2 + bx + c = 0. The program must ask the user to enter the values for a, b and c. It should then determine the discriminant of the parabola and based on the discriminant it should display the real roots: Discriminant = b2 - 4ac > 0 means there will be two distinct real roots. Discriminant = b2 - 4ac = 0 means there will be only one real root. Discriminant = b2 - 4ac < 0 means there will be no real roots. Use the if - then else structure in your program to decide the outcome of the program. User must then use the quadratic equation to solve for x: = − ± √ −

x= -b ±√b²- 4ac/2a

Step-by-step explanation:

ax2 + bx + c = 0

Dividing the quadratic equation by a gives

x2 + b/ax + c/a = 0

x2 + b/ax = - c/a

Applying the square formula

(x)^2 + 2(x) (b/2a) + (b/2a)^2= + (b/2a)^2- c/a

(x+b/2a)^2= b²/4a² - c/a

(x+b/2a)^2= b²/4a² - 4ac/4a²

(x+b/2a)^2= b²- 4ac/4a²

Taking square root of both sides gives

(x+b/2a)= ±√b²- 4ac/2a

x= -b/2a±√b²- 4ac/2a

x= -b ±√b²- 4ac/2a

This is called the quadratic formula and it can solve the value for x for the given value of a, b and c for the quadratic equation.

From this it is concluded that

Discriminant = b2 - 4ac > 0 means there will be two distinct real roots. Discriminant = b2 - 4ac = 0 means there will be only one real root. Discriminant = b2 - 4ac < 0 means there will be no real roots.

This is because a square root of a value greater than 0 is possible and gives two values for roots of x.

The square root of a value less than 0 gives a negative number and therefore the roots are an imaginary number.

The square root of a value greater equal to 0 gives a zero leaving behind only one real root.

I think it is done like this but I am not sure.

Simplifying

9 + -4(2x + -1) = 45

Reorder the terms:

9 + -4(-1 + 2x) = 45

9 + (-1 * -4 + 2x * -4) = 45

9 + (4 + -8x) = 45

Combine like terms: 9 + 4 = 13

13 + -8x = 45

Solving

13 + -8x = 45

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-13' to each side of the equation.

13 + -13 + -8x = 45 + -13

Combine like terms: 13 + -13 = 0

0 + -8x = 45 + -13

-8x = 45 + -13

Combine like terms: 45 + -13 = 32

-8x = 32

Divide each side by '-8'.

x = -4

Simplifying

x = -4