Question 150585
Solve for x:
1) {{{2x*(x+3) = x+25}}} First, perform the indicated distributive property on the left side.
{{{2x^2+6x = x+25}}} Now combine like-terms by subtracting x from both sides.
{{{2x^2+5x = 25}}} Then subtract 25 from both sides.
{{{2x^2+5x-25 = 0}}} Now you have a quadratic equation in standard form that can be solved by factoring.
{{{(2x-5)(x+5) = 0}}} Apply the zero product rule.
{{{2x-5 = 0}}} or {{{x+5 = 0}}}
If {{{2x-5 = 0}}} then {{{2x = 5}}} and {{{x = 5/2}}}
If {{{x+5 = 0}}} then {{{x = -5}}}
The solutions are:
{{{x = 5/2}}}
{{{x = -5}}}
2) {{{3x*(x+3) = 2*(5x+1)}}} First, perform the indicated distributive property on both sides.
{{{3x^2+9x = 10x+2}}} Now combine like-terms by subtracting 10x from both sides.
{{{3x^2-x = 2}}} Then subtract 2 from both sides.
{{{3x^2-x-2 = 0}}} Now you have a quadratic equation that can be solved by factoring.
{{{(3x+2)(x-1) = 0}}} Apply the zero product rule.
{{{3x+2 = 0}}} or {{{x-1 = 0}}}
If {{{3x+2 = 0}}} then {{{3x = -2}}} and {{{x = -2/3}}}
If {{{x-1 = 0}}} then {{{x = 1}}}
The solutions are:
{{{x = -2/3}}}
{{{x = 1}}}
Now this should give you enough clues to do the third problem.
If you still have difficulty then please re-post.