x(x+7)=(2x-1)(x+4)
solving for x? multiply it out, collect terms.
To solve the given equation, we can start by simplifying both sides of the equation. Let's expand the expressions on both sides:
On the left side:
x(x+7) = x * x + x * 7 = x^2 + 7x
On the right side:
(2x-1)(x+4) = (2x) * (x+4) + (-1) * (x+4) = 2x^2 + 8x - x - 4 = 2x^2 + 7x - 4
Now that we have simplified both sides of the equation, we can set them equal to each other:
x^2 + 7x = 2x^2 + 7x - 4
Next, let's move all the terms to one side of the equation:
0 = 2x^2 + 7x - x^2 + 7x - 4
Combining like terms:
0 = x^2 + 14x - 4
This quadratic equation is now in the form: ax^2 + bx + c = 0, where a = 1, b = 14, and c = -4.
To solve the equation, we can use factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:
The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 1, b = 14, and c = -4. Plugging these values into the formula, we get:
x = (-14 ± √(14^2 - 4*1*-4)) / (2*1)
Simplifying further:
x = (-14 ± √(196 + 16)) / 2
x = (-14 ± √212) / 2
Now, let's simplify the square root:
x = (-14 ± √(4 * 53)) / 2
x = (-14 ± 2√53) / 2
We can simplify further by canceling out the common factor of 2:
x = -7 ± √53
Hence, the solutions to the equation x(x+7) = (2x-1)(x+4) are x = -7 + √53 and x = -7 - √53.