Solve by using the quadratic formula
x^2-4x-45=0
To solve the equation x^2 - 4x - 45 = 0 using the quadratic formula, follow these steps:
Step 1: Identify the coefficients of the quadratic equation:
a = 1 (coefficient of x^2)
b = -4 (coefficient of x)
c = -45 (constant term)
Step 2: Substitute the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Step 3: Calculate the discriminant:
Discriminant (D) = b^2 - 4ac
Step 4: Determine the nature of the roots based on the discriminant:
- If D > 0, there are two distinct real roots.
- If D = 0, there is one repeated real root.
- If D < 0, there are no real roots.
Step 5: Apply the quadratic formula and simplify:
x = (-(-4) ± √((-4)^2 - 4(1)(-45))) / 2(1)
x = (4 ± √(16 + 180)) / 2
x = (4 ± √196) / 2
x = (4 ± 14) / 2
Step 6: Simplify the solutions:
x1 = (4 + 14) / 2 = 18 / 2 = 9
x2 = (4 - 14) / 2 = -10 / 2 = -5
Therefore, the solutions to the quadratic equation x^2 - 4x - 45 = 0 are x = 9 and x = -5.
To solve the quadratic equation x^2 - 4x - 45 = 0 using the quadratic formula, we need to identify the values of the coefficients in the equation: a, b, and c.
The quadratic equation is in the standard form ax^2 + bx + c = 0, where:
- a is the coefficient of x^2 term,
- b is the coefficient of x term, and
- c is the constant term.
In this equation, the values of a, b, and c are:
- a = 1 (coefficient of x^2 term),
- b = -4 (coefficient of x term), and
- c = -45 (constant term).
Now, we can substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula, we get:
x = (-(-4) ± √((-4)^2 - 4(1)(-45)))/(2(1))
This simplifies to:
x = (4 ± √(16 + 180)) / 2
Simplifying further:
x = (4 ± √196) / 2
The square root of 196 is 14, so we have:
x = (4 ± 14) / 2
Separating the positive and negative solutions:
x1 = (4 + 14) / 2 = 18 / 2 = 9
and
x2 = (4 - 14) / 2 = -10 / 2 = -5
Therefore, the solutions to the quadratic equation x^2 - 4x - 45 = 0 are x = 9 and x = -5.
Look up the quadratic formula.
x = [-b +/-sqrt(b^2-4ac)]/2a
Then apply it. (a,b,c are the coefficients and constant in the equation)
You should get an integer solution since the equation can easily be foactored to give (x-9)(x+5) = 0
the solutions are 9 and -5.
Hint: b^2 - 4ac = 16 + 180 = 196, which had integer square roots + or - 14.