Find the sum of5x^2-3x+2 and 3x^2-4x-1

Step-by-step explanation:

Simplifying

(3x + -2)(4x + -1) = 0

Reorder the terms:

(-2 + 3x)(4x + -1) = 0

Reorder the terms:

(-2 + 3x)(-1 + 4x) = 0

Multiply (-2 + 3x) * (-1 + 4x)

(-2(-1 + 4x) + 3x * (-1 + 4x)) = 0

((-1 * -2 + 4x * -2) + 3x * (-1 + 4x)) = 0

((2 + -8x) + 3x * (-1 + 4x)) = 0

(2 + -8x + (-1 * 3x + 4x * 3x)) = 0

(2 + -8x + (-3x + 12x2)) = 0

Combine like terms: -8x + -3x = -11x

(2 + -11x + 12x2) = 0

Solving

2 + -11x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.

(1 + -4x)(2 + -3x) = 0

Subproblem 1

Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying

1 + -4x = 0

Solving

1 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0

0 + -4x = 0 + -1

-4x = 0 + -1

Combine like terms: 0 + -1 = -1

-4x = -1

Divide each side by '-4'.

x = 0.25

Simplifying

x = 0.25

Subproblem 2

Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying

2 + -3x = 0

Solving

2 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.

2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0

0 + -3x = 0 + -2

-3x = 0 + -2

Combine like terms: 0 + -2 = -2

-3x = -2

Divide each side by '-3'.

x = 0.6666666667

Simplifying

x = 0.6666666667

Solution

x = {0.25, 0.6666666667}

2.) 5x^2-3x=2

We move all terms to the left:

5x^2-3x-(2)=0

a = 5; b = -3; c = -2;

Δ = b2-4ac

Δ = -32-4·5·(-2)

Δ = 49

The delta value is higher than zero, so the equation has two solutions

We use following formulas to calculate our solutions:

x1=−b−Δ√2ax2=−b+Δ√2a

Δ−−√=49−−√=7

x1=−b−Δ√2a=−(−3)−72∗5=−410=−2/5

x2=−b+Δ√2a=−(−3)+72∗5=1010=1