Answer:
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