Problem 14 - College Algebra

Question

Solve each equation in Exercises \(1-14\) by factoring. $$10 x-1=(2 x+1)^{2}$$

Step-by-Step Solution

Answer

-0.5 and 1 are the solutions to the given equation.

Step 1: Expand the Squared Term

Expand the right hand side of the equation \((2x + 1)^2\). After expansion, equation becomes \(4x^2 + 4x + 1 = 10x - 1\).

Step 2: Rewrite in Standard Quadratic Form

Rewrite the equation in standard quadratic form \(ax^2 + bx + c = 0\) by taking all terms to one side. Equation becomes \(4x^2 - 6x +2 = 0\).

Step 3: Factor the Quadratic Equation

Now factor this equation to find the roots or solutions. The equation \(4x^2 - 6x +2 = 0\), cannot be factored further, so we can use the quadratic formula to find solutions. The quadratic formula is \(-\frac{b}{2a} ± \frac{\sqrt{b^2-4ac}}{2a}\). After substituting we will have the two solutions for this equation.