Question

Solve the equation by factoring, by finding square roots, or by using the quadratic formula. $$20 d^{2}-10 d=100$$

Short answer

The solutions of the equation \(20 d^{2}-10 d=100\) are \(d=2.5\) and \(d=-2\)

Step-by-step solution

Set the Equation to Equal Zero

The first step in solving a quadratic equation is to always set the equation to equal zero. Do this by subtracting 100 from both sides of the equation: \(20d^2-10d-100= 0\)

Factor Out the Common Factor

Notice that 10 is a common factor of all coefficients. Let's factor it out: \(10(2d^2-d-10)= 0\)

Simplify the Quadratic

Making the equation simpler, you will end up with \(2d^2-d-10 = 0\)

Further Factor if Possible

Now, we need to factorize the equation further if possible. Factoring \(2d^2-d-10 = 0\) gives \((2d-5)(d+2) = 0\)

Solve for \(d\)

Finally, we set our two factors equal to zero and solve for \(d\). So, \(2d-5=0\) gives \(d=\frac{5}{2}\) (or 2.5) and \(d+2 = 0\) gives \(d= -2\)