Solve for x 2x^2-3x-20=x^2+34

$2 x^{2} - 3 x - 20 = x^{2} + 34$

Step 1

Move all terms containing $x$ to the left side of the equation.

Subtract $x^{2}$ from both sides of the equation.

$2 x^{2} - 3 x - 20 - x^{2} = 34$

Subtract $x^{2}$ from $2 x^{2}$ .

$x^{2} - 3 x - 20 = 34$

Step 2

Subtract $34$ from both sides of the equation.

$x^{2} - 3 x - 20 - 34 = 0$

Step 3

Subtract $34$ from $- 20$ .

$x^{2} - 3 x - 54 = 0$

Step 4

Factor $x^{2} - 3 x - 54$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 54$ and whose sum is $- 3$ .

$- 9, 6$

Write the factored form using these integers.

$(x - 9) (x + 6) = 0$

Step 5

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

$x - 9 = 0$

$x + 6 = 0$

Step 6

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

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

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Step 7

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

Step 8

The final solution is all the values that make $(x - 9) (x + 6) = 0$ true.

$x = 9, - 6$

Solve for x 2x^2-3x-20=x^2+34

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