Find the measure of each angle
(x + 1) (4x - 56)
(X+1)(4X-56).
4X^2 - 56X + 4X - 56,
Combine like-terms:
4X^2 - 52X - 56,
Factor:
4(X^2 - 13X - 14).
To find the measure of each angle in the expression (x + 1)(4x - 56), we need to express the expression as an equation and then solve for x.
Step 1: Multiply the two binomials using the distributive property.
(x + 1)(4x - 56) = 4x^2 - 56x + 4x - 56
Simplifying further, we get:
= 4x^2 - 52x - 56
Step 2: Set the equation equal to zero:
4x^2 - 52x - 56 = 0
Step 3: Solve the quadratic equation.
To solve this quadratic equation, we can either factorize or use the quadratic formula. In this case, factoring may be a bit challenging, so let's use the quadratic formula.
The quadratic formula is: x = (-b ± √(b^2 - 4ac)) / 2a
For our equation, a = 4, b = -52, and c = -56. Substituting these values into the formula, we get:
x = (-(-52) ± √((-52)^2 - 4(4)(-56))) / (2(4))
x = (52 ± √(2704 + 896)) / 8
x = (52 ± √3600) / 8
x = (52 ± 60) / 8
Simplifying further, we get two possible solutions:
x = (52 + 60) / 8 = 112 / 8 = 14
x = (52 - 60) / 8 = -8 / 8 = -1
Step 4: Find the measure of each angle.
Now that we have the value of x, we can substitute it back into the original expression to find the measure of each angle.
For x = 14:
Angle 1 = x + 1 = 14 + 1 = 15
Angle 2 = 4x - 56 = 4(14) - 56 = 56 - 56 = 0
For x = -1:
Angle 1 = x + 1 = -1 + 1 = 0
Angle 2 = 4x - 56 = 4(-1) - 56 = -4 - 56 = -60
Therefore, the measures of the angles depend on the value of x:
For x = 14: Angle 1 = 15, Angle 2 = 0
For x = -1: Angle 1 = 0, Angle 2 = -60