Use factoring to solve each equation.
(x+6)(x+5)=2
x=-5 or x=-6
To solve the equation (x+6)(x+5) = 2 using factoring, we can start by expanding the left side:
(x+6)(x+5) = (x+6)x + (x+6)5 = x^2 + 6x + 5x + 30 = x^2 + 11x + 30.
Now, we have x^2 + 11x + 30 = 2.
To solve this equation by factoring, we can set it equal to zero by subtracting 2 from both sides:
x^2 + 11x + 30 - 2 = 0,
x^2 + 11x + 28 = 0.
Now, we need to find two numbers that add up to 11 and multiply to 28. After some trial and error, we can see that the numbers are 4 and 7.
So, we can rewrite the equation as:
(x + 4)(x + 7) = 0.
Now, to find the solutions, we set each factor equal to zero:
x + 4 = 0,
x = -4.
x + 7 = 0,
x = -7.
Therefore, the solutions to the equation (x+6)(x+5) = 2 are x = -4 and x = -7.
To solve the equation (x+6)(x+5) = 2 using factoring, we need to express the left side of the equation as a product of two binomials.
First, let's distribute the factors on the left side:
(x+6)(x+5) = 2
x^2 + 6x + 5x + 30 = 2
x^2 + 11x + 30 = 2
Now, we can move all terms to one side of the equation to make it equal to zero:
x^2 + 11x + 30 - 2 = 0
x^2 + 11x + 28 = 0
To factor this quadratic equation, we need to find two numbers that multiply to give 28 and add up to 11 (the coefficient of x). In this case, the numbers are 4 and 7, because 4 * 7 = 28 and 4 + 7 = 11.
So, we can rewrite the equation by splitting the middle term using these numbers:
x^2 + 4x + 7x + 28 = 0
Now, group the terms:
(x^2 + 4x) + (7x + 28) = 0
Factor out the common factor from each binomial:
x(x + 4) + 7(x + 4) = 0
Now, notice that (x + 4) is a common factor in both terms. We can factor it out:
(x + 4)(x + 7) = 0
Now, we have factored the original equation (x+6)(x+5) = 2 into two binomials: (x + 4) and (x + 7) equaled to zero.
To solve for x, we set each factor equal to zero and solve for x:
x + 4 = 0 or x + 7 = 0
Solving each equation separately:
For x + 4 = 0:
x = -4
For x + 7 = 0:
x = -7
So, the solutions to the equation (x+6)(x+5) = 2 are x = -4 and x = -7.