SOLUTION: Solve the following equations: a: x^3-4x=0 b: 2x^2+7x-15=0

Algebra ->  Algebra  -> Equations -> SOLUTION: Solve the following equations: a: x^3-4x=0 b: 2x^2+7x-15=0      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 148495: Solve the following equations:
a: x^3-4x=0
b: 2x^2+7x-15=0
Answer by jim_thompson5910(28504) About Me  (Show Source):
You can put this solution on YOUR website!
a)

x%5E3-4x=0 Start with the given equation.


x%28x%5E2-4%29=0 Factor out the GCF x


x%28x%2B2%29%28x-2%29=0 Factor x%5E2-4 to get %28x%2B2%29%28x-2%29


Now set each factor equal to zero:

x=0, x%2B2=0 or x-2=0


Now solve for x for each factor:

x=0, x=-2 or x=2


So the solutions of x%5E3-4x=0 are x=0, x=-2 or x=2





b)

2x%5E2%2B7x-15=0 Start with the given equation.


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%287%29+%2B-+sqrt%28+%287%29%5E2-4%282%29%28-15%29+%29%29%2F%282%282%29%29 Plug in a=2, b=7, and c=-15


x+=+%28-7+%2B-+sqrt%28+49-4%282%29%28-15%29+%29%29%2F%282%282%29%29 Square 7 to get 49.


x+=+%28-7+%2B-+sqrt%28+49--120+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-15%29 to get -120


x+=+%28-7+%2B-+sqrt%28+49%2B120+%29%29%2F%282%282%29%29 Rewrite sqrt%2849--120%29 as sqrt%2849%2B120%29


x+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%282%282%29%29 Add 49 to 120 to get 169


x+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-7+%2B-+13%29%2F%284%29 Take the square root of 169 to get 13.


x+=+%28-7+%2B+13%29%2F%284%29 or x+=+%28-7+-+13%29%2F%284%29 Break up the expression.


x+=+%286%29%2F%284%29 or x+=++%28-20%29%2F%284%29 Combine like terms.


x+=+3%2F2 or x+=+-5 Simplify.


So our answers are x+=+3%2F2 or x+=+-5