Question
Factor to solve the equation 4x^2+12x+5=−4
Answers
Answered by
GPT 3.5
To solve the given equation, first let's gather all the terms on one side of the equation:
4x^2 + 12x + 5 + 4 = 0
Simplifying:
4x^2 + 12x + 9 = 0
Now, let's find the factors of the quadratic equation. Since the coefficient of x^2 is 4 and the constant term is 9, the factors will be in the form of (4x + m)(x + n), where m and n are integers.
Let's find the values of m and n by considering the factorization of 4 * 9 = 36. The factors of 36 that can be expressed in the form of 4x + m and x + n are:
(4, 9), (-4, -9), (1, 36), (-1, -36), (2, 18), (-2, -18), (3, 12), (-3, -12), (6, 6), (-6, -6)
Since we need to find factors that add up to 12 (from 12x term), the solutions are (3, 12) and (-3, -12).
Therefore, the factors of the given equation are:
(4x + 3)(x + 3) = 0
Setting each factor equal to zero:
4x + 3 = 0 or x + 3 = 0
Solving each equation:
4x = -3 or x = -3
x = -3/4 or x = -3
Therefore, the solutions to the equation 4x^2 + 12x + 5 = −4 are x = -3/4 and x = -3.
4x^2 + 12x + 5 + 4 = 0
Simplifying:
4x^2 + 12x + 9 = 0
Now, let's find the factors of the quadratic equation. Since the coefficient of x^2 is 4 and the constant term is 9, the factors will be in the form of (4x + m)(x + n), where m and n are integers.
Let's find the values of m and n by considering the factorization of 4 * 9 = 36. The factors of 36 that can be expressed in the form of 4x + m and x + n are:
(4, 9), (-4, -9), (1, 36), (-1, -36), (2, 18), (-2, -18), (3, 12), (-3, -12), (6, 6), (-6, -6)
Since we need to find factors that add up to 12 (from 12x term), the solutions are (3, 12) and (-3, -12).
Therefore, the factors of the given equation are:
(4x + 3)(x + 3) = 0
Setting each factor equal to zero:
4x + 3 = 0 or x + 3 = 0
Solving each equation:
4x = -3 or x = -3
x = -3/4 or x = -3
Therefore, the solutions to the equation 4x^2 + 12x + 5 = −4 are x = -3/4 and x = -3.