SOLUTION: Please help. Solve for x. The square root of 2x+7 plus x=4. thanks for your help.

Algebra ->  Equations -> SOLUTION: Please help. Solve for x. The square root of 2x+7 plus x=4. thanks for your help.      Log On


   



Question 937678: Please help. Solve for x. The square root of 2x+7 plus x=4. thanks for your help.
Found 2 solutions by TimothyLamb, MathLover1:
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(2x+7)+ x = 4
sqrt(2x+7) = -x + 4
( sqrt(2x+7) )^2 = (-x + 4)^2
2x + 7 = xx - 8x + 16
xx - 10x + 9 = 0
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the above quadratic equation is in standard form, with a=1, b=-10 and c=9
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -10 9
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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x = 9
x = 1
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answer:
both values of x are valid solutions to the problem ...
x = 9
x = 1
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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%2B7%29+%2B+x=4
sqrt%282x%2B7%29=4-x ........square both sides
%28sqrt%282x%2B7%29%29%5E2=%284-x%29%5E2
2x%2B7=4%5E2-8x%2Bx%5E2
2x%2B7=16-8x%2Bx%5E2
0=16-8x-2x-7%2Bx%5E2
x%5E2-10x%2B9=0 ....factor completely, write -10x as -x-9x
x%5E2-x-9x%2B9=0 ...group
%28x%5E2-x%29-%289x-9%29=0
x%28x-1%29-9%28x-1%29=0
%28x-9%29%28x-1%29=0

solutions:
if %28x-9%29=0=> highlight%28x=9%29
if %28x-1%29=0=> highlight%28x=1%29

+graph%28+600%2C+600%2C+-10%2C+15%2C+-15%2C+15%2C+x%5E2-10x%2B9%29+