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Q. 1

Expert-verified
Found in: Page 870

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Solve:$3{x}^{2}-2x=-1$

The value of $x=1±i\sqrt{2}$

See the step by step solution

## Step 1. Given information.

$3{x}^{2}-2x=-1$

We can rewrite the equation as:

$3{x}^{2}-2x+1=0$

## Step 2. Find solution of x.

By comparing $3{x}^{2}-2x+1=0$, with standard quadratic equation: $a{x}^{2}+bx+c=0$.

We get,

$a=3\phantom{\rule{0ex}{0ex}}b=-2\phantom{\rule{0ex}{0ex}}c=1$

Substitute these values in the formula and solve.

$x=\frac{-\left(-2\right)±\sqrt{{\left(-2\right)}^{2}-4\left(3\right)\left(1\right)}}{2\left(1\right)}\phantom{\rule{0ex}{0ex}}x=\frac{2±\sqrt{4-12}}{2}\phantom{\rule{0ex}{0ex}}x=\frac{2±\sqrt{-8}}{2}\phantom{\rule{0ex}{0ex}}x=\frac{2±\sqrt{8{i}^{2}}}{2}\phantom{\rule{0ex}{0ex}}x=\frac{2±i2\sqrt{2}}{2}\phantom{\rule{0ex}{0ex}}x=\frac{2\left(1±i\sqrt{2}\right)}{2}\phantom{\rule{0ex}{0ex}}x=1±i\sqrt{2}$