Factor to solve the equation 4x2+12x+5=−4.(1 point)
x=−2/3
x=1 1/2
x=2/3
x=−1 1/2
To solve the equation 4x^2 + 12x + 5 = -4, we can rewrite it as 4x^2 + 12x + 9 = 0 by adding 4 to both sides of the equation.
Next, we can factor the quadratic expression 4x^2 + 12x + 9.
When factoring, we look for two numbers whose product is 4 * 9 = 36 and whose sum is 12. The numbers that meet these criteria are 6 and 6 since 6 * 6 = 36 and 6 + 6 = 12. Therefore, we can rewrite the equation as:
(2x + 3)(2x + 3) = 0
Now, we can set each factor equal to zero and solve for x:
2x + 3 = 0
2x = -3
x = -3/2
Thus, the solution to the equation 4x^2 + 12x + 5 = -4 is:
x = -3/2 or -1.5.
To factor the quadratic equation 4x^2 + 12x + 5 = -4, we first rearrange the equation to set it equal to zero:
4x^2 + 12x + 9 = 0
Next, let's factorize the equation by finding two numbers that multiply to 4 (the coefficient of x^2) and add up to 12 (the coefficient of x):
The numbers 3 and 3 satisfy these conditions, so the factored form of the equation is:
(2x + 3)(2x + 3) = 0
Now, we can solve for x by setting each factor equal to zero:
2x + 3 = 0
Solving for x, we have:
x = -3/2
Therefore, the correct factorized solution is:
x = -3/2