Questions on Algebra: Quadratic Equation answered by real tutors!

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Use the distributive property to multiply the first part of the equation.
2x^2+6x=x+25
subtract x from both sides
2x^2+5x=25
Subtract 25 from both sides
2x^2+5x-25=0
this is a quadratic equation

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ax^2+bx+c=0

(in our case 2x^2+5x+-25 = 0

) has the following solutons:

$x[12] = (b+-sqrt( b^2-4ac ))/2\a$

For these solutions to exist, the discriminant b^2-4ac

should not be a negative number.

First, we need to compute the discriminant b^2-4ac

.

Discriminant d=225 is greater than zero. That means that there are two solutions: $x[12] = (-5+-sqrt( 225 ))/2\a$ .

$x[1] = (-(5)+sqrt( 225 ))/2\2 = 2.5$
$x[2] = (-(5)-sqrt( 225 ))/2\2 = -5$

Quadratic expression 2x^2+5x+-25

can be factored:
2x+5x+-25 = 2(x-2.5)*(x--5)

Again, the answer is: 2.5, -5. Here's your graph:
graph( 500, 500, -10, 10, -20, 20, 2*x^2+5*x+-25 )