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Chapter 1: Problem 14

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

Short Answer

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

Step by step solution

01

Expand the Squared Term

Expand the right hand side of the equation \((2x + 1)^2\). After expansion, equation becomes \(4x^2 + 4x + 1 = 10x - 1\).
02

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 \(4x^2 - 6x +2 = 0\).
03

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 \(-\frac{b}{2a} 卤 \frac{\sqrt{b^2-4ac}}{2a}\). After substituting we will have the two solutions for this equation.

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Most popular questions from this chapter

In Exercises \(69-72,\) use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$ \frac{1}{(x-2)^{2}}>0 $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\frac{-12+\sqrt{-28}}{32}$$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(3+5 i)(3-5 i)$$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$(-5-\sqrt{-9})^{2}$$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x^{2}-x-2}{x^{2}-4 x+3}>0 $$
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