Which are solutions of the equation 4x² - 7x = 3x + 24? Check all that apply.
x = - 4, x = - 3, x = - 3/2, x = 2/3, x = 2, x = 4

Solution:

Given is a quadratic equation 4x² - 10 x - 24 = 0

Taking 2 as common outside we have 2(2x² - 5x - 12) = 0.

Now, factorize the quadratic equation 2x² - 5x - 12 to find the value of x by splitting the middle term.

Step 1: Identify the values of a, b and c.

In the above equation, a is coefficient of x² = 2, b is the coefficient of x = - 5 and c is the constant term = - 12.

Step 2: Multiply a and c and find the factors that add up to b.

2 × (- 12) = - 24

⇒ - 8 and 3 are the factors that add up to b.

Step 3: Split bx into two terms.

2x² - 8x + 3x - 12 = 0

Step 4: Take out the common factors by grouping.

2x (x - 4) + 3 (x - 4) = 0

(2x + 3)(x - 4) = 0

By putting the factors equal to zero we get two values of x

x - 4 = 0 and 2x + 3 = 0

x = 4 and x = -3/2

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Which are solutions of the equation 4x² - 7x = 3x + 24? Check all that apply.
x = - 4, x = - 3, x = - 3/2, x = 2/3, x = 2, x = 4

Summary:

x = 4 and x= -3/2 are the solutions that apply to the equation 4x² - 10x - 24 = 0.