Quadratic Equation prob: x - 10 - 20 square root (x - 2) +

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
DrO
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Quadratic Equation prob: x - 10 - 20 square root (x - 2) +

How do you attempt a problem like this?

x - 10 - 20 square root (x - 2) + 30 = 0

Sorry I recently joined and don't know how to put the square root sign in. There is a square root sign above the (x - 2). If someone can tell me how to put in the square root sign I will repost the question.

Martingale
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DrO wrote:How do you attempt a problem like this?

x - 10 - 20 square root (x - 2) + 30 = 0

Sorry I recently joined and don't know how to put the square root sign in. There is a square root sign above the (x - 2). If someone can tell me how to put in the square root sign I will repost the question.

$x-10-20\sqrt{x-2}+30=0$

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$$x-10-20\sqrt{x-2}+30=0$$

Martingale
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DrO wrote:How do you attempt a problem like this?

x - 10 - 20 square root (x - 2) + 30 = 0

Sorry I recently joined and don't know how to put the square root sign in. There is a square root sign above the (x - 2). If someone can tell me how to put in the square root sign I will repost the question.

try letting $u=\sqrt{x-2}$

stapel_eliz
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DrO wrote:How do you attempt a problem like this?

x - 10 - 20 square root (x - 2) + 30 = 0

A good first step for solving radical equations is to try to isolate the radical:

. . . . .$x\, -\, 10\, -\, 20\sqrt{x\, -\, 2}\, +\, 30\, =\, 0$

. . . . .$x\, -\, 10\, +\, 30\, =\, 20\sqrt{x\, -\, 2}$

. . . . .$x\, +\, 20\, =\, 20\sqrt{x\, -\, 2}$

Then square both sides:

. . . . .$(x\, +\, 20)^2\, =\, \left(20\sqrt{x\, -\, 2}\right)^2$

Keep in mind that (x + 20)2 means (x + 20)(x + 20), and multiply out the square:

. . . . .$x^2\, +\, 40x\, +\, 400\, =\, 400(x\, -\, 2)$

. . . . .$x^2\, +\, 40x\, +\, 400\, =\, 400x\, -\, 800$

Then gather everything together onto one side:

. . . . .$x^2\, +\, 40x\, -\, 400x\, +\, 400\, +\, 800\, =\, 0$

Simplify, and then solve the quadratic by whatever method you prefer.

Martingale
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Martingale wrote:
DrO wrote:How do you attempt a problem like this?

x - 10 - 20 square root (x - 2) + 30 = 0

Sorry I recently joined and don't know how to put the square root sign in. There is a square root sign above the (x - 2). If someone can tell me how to put in the square root sign I will repost the question.

try letting $u=\sqrt{x-2}$

using the substitution above you can also solve the equation

$u=\sqrt{x-2}\Rightarrow u^2=x-2\Rightarrow u^2+2=x$

substituting back into your equation you get...

$x - 10 - 20 \sqrt{x - 2} + 30 = 0\Rightarrow u^2+2-10-20u+30=0$

simplify and solve for u ... and then for x