Solve each quadratic equation. If roots are not real, use i i . 2 x 2 + 18 = 0 2x^2+18=0

Here, we're going to solve this quadratic equation using our square root property. So we want to isolate x to find what value of x makes this equation true. So let's start by subtracting 18 from both sides of our equation. So we get two x squared is equal to negative 18. Next we're going to divide both sides by two. So we have x squared is equal to negative nine. Now that we have our quantity squared is equal to some value, we can apply our square root property. So we'll square root both sides, so that our square root and square cancel out. And we have x is equal to positive and negative square root of nine. Next, we need to simplify this radical and use I if necessary. Using our product property, we know that we can split this up and think of it as the square root of nine times the square root of negative one. And we know that the square root of nine is three and that the square root of negative one is I. So our final answer can be written as x is equal to both positive and negative three I.

Solve each quadratic equation. If roots are not real, use i i . 2 x 2 + 18 = 0 2x^2+18=0

x = ± 9 2 x=\pm\frac92 x = ± 2 9

x = ± 9 2 i x=\pm\frac92i x = ± 2 9 i

10. Quadratic Equations and Functions

The Square Root Property

Intermediate Algebra

10. Quadratic Equations and Functions

The Square Root Property

Struggling with Intermediate Algebra?

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Multiple Choice

Solve each quadratic equation. If roots are not real, use $i$ .
$2 x^{2} + 18 = 0$

$x=\pm3$

$x=\pm\frac92$

$x=\pm3i$

$x=\pm\frac92i$

Verified step by step guidance

Start with the given quadratic equation: \$2x^2 + 18 = 0$.

Isolate the $x^2$ term by subtracting 18 from both sides: \$2x^2 = -18$.

Divide both sides by 2 to solve for $x^2$: $x^2 = \frac{-18}{2}$.

Simplify the right side: $x^2 = -9$.

Take the square root of both sides, remembering to include the imaginary unit $i$ for negative values under the square root: $x = \pm \sqrt{-9} = \pm 3i$.

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Struggling with Intermediate Algebra?

Solve each quadratic equation. If roots are not real, use ii. 2x2+18=02x^2+18=0

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Solve each quadratic equation. If roots are not real, use $i$ .
$2 x^{2} + 18 = 0$