solve 8x(4x+4)=28
x=?
32x^2 + 32x - 28 = 0
8x^2 + 8x - 7 = 0
It does not factor, so use the quadratic formula to continue.
wow, forgot the term, sorry.
8x-(4x+4)=28
To solve the equation 8x(4x+4)=28 for x, we'll need to follow these steps:
Step 1: Distribute
Distribute the 8x to both terms inside the parentheses: 32x^2 + 32x = 28.
Step 2: Rearrange the equation
To solve a quadratic equation, we need to have the equation in the form ax^2 + bx + c = 0. Therefore, we have to move all the terms to one side of the equation: 32x^2 + 32x - 28 = 0.
Step 3: Simplify
If we simplify the equation further, we get: 8x^2 + 8x - 7 = 0.
Step 4: Solve the quadratic equation
To solve the quadratic equation, we can use either factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:
The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / (2a).
For our equation 8x^2 + 8x - 7 = 0, a = 8, b = 8, and c = -7.
Plugging these values into the quadratic formula, we get:
x = (-8 ± √(8^2 - 4(8)(-7))) / (2(8)).
Simplifying further:
x = (-8 ± √(64 + 224)) / 16,
x = (-8 ± √(288)) / 16.
Step 5: Simplify the square root
Since 288 can be simplified as 144 * 2, we can rewrite the equation as:
x = (-8 ± √(144 * 2)) / 16,
x = (-8 ± 12√2) / 16.
Step 6: Simplify the fraction
Next, we can simplify the fraction by dividing both the numerator and denominator by 4:
x = (-2 ± 3√2) / 4.
Therefore, the two solutions for x are:
x = (-2 + 3√2) / 4, and
x = (-2 - 3√2) / 4.