solve a perfect square trinomial equation.
(4x+1)(x+4)=49
Rewrite it by multiplying it out, and factor.
4x^2 + 17x -45 = 0.
I don't see any "perfect square" here.
It also does not factor easily. Use the quadratic equation.
x = [-17 +/- sqrt(1009)]/8
x = 1.846 is one of the two solutions
To solve the given perfect square trinomial equation (4x+1)(x+4) = 49, follow these steps:
Step 1: Expand the equation
(4x+1)(x+4) = 49
4x^2 + 16x + x + 4 = 49
4x^2 + 17x + 4 = 49
Step 2: Rearrange the equation in standard form
4x^2 + 17x + 4 - 49 = 0
4x^2 + 17x - 45 = 0
Step 3: Check the coefficient of x^2 (in this case, 4). If it is not 1, divide the entire equation by that coefficient. However, in this equation, the coefficient is already 1, so we don't need to perform this step.
Step 4: Factorize the trinomial
To factorize the quadratic equation, we need to find two numbers that multiply to give the product of 4 (-45) and add up to the coefficient of x (17). The two numbers in this case are 20 and -3.
4x^2 + 17x - 45 = 0
4x^2 + 20x - 3x - 45 = 0
(4x^2 + 20x) + (-3x - 45) = 0
4x(x + 5) - 3(x + 5) = 0
(4x - 3)(x + 5) = 0
Step 5: Set each factor equal to zero and solve
By setting each factor equal to zero, we can solve for the values of x:
4x - 3 = 0 or x + 5 = 0
For 4x - 3 = 0:
4x = 3
x = 3/4
For x + 5 = 0:
x = -5
Therefore, the solutions to the perfect square trinomial equation are x = 3/4 and x = -5.