Use factoring to solve the equation:
x^2+13x+36+0
That is not an equation. Perhaps you mean
x^2 + 13x + 36 = 0
which IS an equation.
It can be factored as
(x+9)(x+4) = 0
So the answers are x=-9 and x=-4
Those two values of x make on or the other factor equal to zero, so they are solutions.
To solve the equation x^2 + 13x + 36 = 0 using factoring, we need to find two numbers that multiply to 36 (the constant term) and add up to 13 (the coefficient of the x-term).
Let's break down the problem step by step:
Step 1: Gather the given equation.
x^2 + 13x + 36 = 0
Step 2: Identify the values of a, b, and c.
The quadratic equation is in the form ax^2 + bx + c = 0.
In this case, a = 1, b = 13, and c = 36.
Step 3: Find two numbers that multiply to c (36) and add up to b (13).
To factorize the quadratic equation, we need to find two numbers. Let's list down the factor pairs of 36:
1 * 36 = 36
2 * 18 = 36
3 * 12 = 36
4 * 9 = 36
6 * 6 = 36
Among these factor pairs, only 4 and 9 add up to 13.
Hence, we can rewrite the middle term of the quadratic equation as 4x + 9x.
Step 4: Rewrite the quadratic equation.
x^2 + 13x + 36 = 0
(x^2 + 4x) + (9x + 36) = 0
Step 5: Group the terms and factor by grouping.
(x^2 + 4x) + (9x + 36) = 0
x(x + 4) + 9(x + 4) = 0
Step 6: Factor out the common binomial factor.
(x + 4)(x + 9) = 0
Step 7: Set each binomial factor equal to zero and solve for x.
x + 4 = 0 or x + 9 = 0
Step 8: Solve for x.
For x + 4 = 0:
x = -4
For x + 9 = 0:
x = -9
Step 9: Final solution.
The solutions to the equation x^2 + 13x + 36 = 0 are x = -4 and x = -9.
Therefore, the equation is satisfied when x equals -4 or -9.