Solve for x square root of 2x^2+17x=3

$\sqrt{2 x^{2} + 17 x} = 3$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{2 x^{2} + 17 x}}^{2} = 3^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x^{2} + 17 x}$ as ${(2 x^{2} + 17 x)}^{\frac{1}{2}}$ .

${({(2 x^{2} + 17 x)}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

Simplify ${({(2 x^{2} + 17 x)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 x^{2} + 17 x)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(2 x^{2} + 17 x)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x^{2} + 17 x)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(2 x^{2} + 17 x)}^{1} = 3^{2}$

Simplify.

$2 x^{2} + 17 x = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$2 x^{2} + 17 x = 9$

Step 3

Solve for $x$ .

Subtract $9$ from both sides of the equation.

$2 x^{2} + 17 x - 9 = 0$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot - 9 = - 18$ and whose sum is $b = 17$ .

Factor $17$ out of $17 x$ .

$2 x^{2} + 17 (x) - 9 = 0$

Rewrite $17$ as $- 1$ plus $18$

$2 x^{2} + (- 1 + 18) x - 9 = 0$

Apply the distributive property.

$2 x^{2} - 1 x + 18 x - 9 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 1 x) + 18 x - 9 = 0$

Factor out the greatest common factor (GCF) from each group.

$x (2 x - 1) + 9 (2 x - 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$(2 x - 1) (x + 9) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 x - 1 = 0$

$x + 9 = 0$

Set $2 x - 1$ equal to $0$ and solve for $x$ .

Set $2 x - 1$ equal to $0$ .

$2 x - 1 = 0$

Solve $2 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$2 x = 1$

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Set $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

The final solution is all the values that make $(2 x - 1) (x + 9) = 0$ true.

$x = \frac{1}{2}, - 9$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}, - 9$

Decimal Form:

$x = 0.5, - 9$

Solve for x square root of 2x^2+17x=3

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