/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 48 Solve each quadratic equation us... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 48

Solve each quadratic equation using the quadratic formula. Express solutions in standard form. $$2 x^{2}+2 x+3=0$$

Short Answer

Expert verified
The solutions to the given quadratic equation \(2x^2 + 2x + 3 = 0\) are \(x = -1/2 + \sqrt{5}i/2\) and \(x = -1/2 - \sqrt{5}i/2\).

Step by step solution

01

Identify a, b and c

Identify the coefficients \(a\), \(b\) and \(c\) from the given quadratic equation. Here, \(a = 2\), \(b = 2\), and \(c = 3\).
02

Substitute a, b and c into the quadratic formula

The quadratic formula is \(-b 卤 鈭�(b^2 - 4ac) / 2a\). Substituting the values of \(a\), \(b\) and \(c\) from Step 1 we get \[ x = \frac{-b 卤鈭歿(b^2-4ac)}}{2a} = \frac{-2 卤鈭歿(2^2 - 4*2*3)}}{2*2} = \frac{-2 卤鈭歿(4 - 24)}}{4}\]
03

Simplify the expression inside the square root

Perform the operation inside the square root. \[ x = \frac{-2 卤鈭歿-20}}{4} \]
04

Write the square root of negative number

We note that the term inside the square root is negative. The square root of negative number can be written as 'i' times the square root of that number. So \[ x = \frac{-2 卤鈭歿20}i}{4} \]
05

Simplify the fraction

We can simplify the fraction in the equation by dividing every term by the common factor of 2. So the final solutions in standard form are \[ x = \frac{-1 卤鈭歿5}i}{2} \]

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