Solve the quadratic by factoring.
5, x, squared, plus, 9, x, minus, 4, equals, 3, x, plus, 4
5x
2
+9x−4=3x+4
To solve the quadratic by factoring, we want to rearrange the equation so that one side is equal to zero.
Starting with the given equation:
5x^2 + 9x - 4 = 3x + 4
First, let's move all terms to one side:
5x^2 + 9x - 3x - 4 - 4 = 0
Combining like terms:
5x^2 + 6x - 8 = 0
To factor this quadratic equation, we need to find two numbers that multiply to get -8 and add to get 6. The numbers are 8 and -1.
Now we can rewrite the equation:
(5x - 1)(x + 8) = 0
Setting each factor equal to zero:
5x - 1 = 0 or x + 8 = 0
Solving for x in each equation:
5x = 1 or x = -8
x = 1/5 or x = -8
Therefore, the solutions to the quadratic equation 5x^2 + 9x - 4 = 3x + 4 are x = 1/5 and x = -8.
To solve the quadratic equation 5x^2 + 9x - 4 = 3x + 4 by factoring, you can follow these steps:
Step 1: Rewrite the equation in standard quadratic form:
5x^2 + 9x - 4 - (3x + 4) = 0
Step 2: Combine like terms to get a simplified equation:
5x^2 + 9x - 3x - 8 = 0
Step 3: Group the terms in pairs:
(5x^2 + 9x) - (3x + 8) = 0
Step 4: Factor out a common factor from each pair:
x(5x + 9) - 1(3x + 8) = 0
Step 5: Simplify the equation further:
(5x + 9)(x - 1) = 0
Step 6: Set each factor equal to zero and solve for x:
5x + 9 = 0 => 5x = -9 => x = -9/5
x - 1 = 0 => x = 1
So the solutions to the quadratic equation are x = -9/5 and x = 1.
To solve the quadratic equation by factoring, we need to make one side of the equation equal to zero. Let's rearrange the equation:
5x^2 + 9x - 4 = 3x + 4
First, let's gather all the terms on one side of the equation:
5x^2 + 9x - 3x - 4 - 4 = 0
Simplifying further:
5x^2 + 6x - 8 = 0
Now, we'll look for two numbers that multiply to give -8 and add up to 6. These numbers are 8 and -1.
Next, we'll split the middle term (6x) using the two numbers we found:
5x^2 + 8x - x - 8 = 0
Now, we'll factor by grouping:
(5x^2 + 8x) - (x + 8) = 0
Factor out the common terms:
x(5x + 8) - 1(5x + 8) = 0
Now, notice that we have a common factor of (5x + 8), so we can factor it out:
(5x + 8)(x - 1) = 0
Now, we have two factors: (5x + 8) and (x - 1). To find the values of x, we set each factor equal to zero and solve for x:
Setting (5x + 8) = 0:
5x + 8 = 0
5x = -8
x = -8/5
Setting (x - 1) = 0:
x - 1 = 0
x = 1
Therefore, the solutions to the quadratic equation 5x^2 + 9x - 4 = 3x + 4 are x = -8/5 and x = 1.