x²-15x-45000{please solve this instantly}
Answers
Step-by-step explanation:
Simplifying
x2 + -15x + -45000 = 0
Reorder the terms:
-45000 + -15x + x2 = 0
Solving
-45000 + -15x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '45000' to each side of the equation.
-45000 + -15x + 45000 + x2 = 0 + 45000
Reorder the terms:
-45000 + 45000 + -15x + x2 = 0 + 45000
Combine like terms: -45000 + 45000 = 0
0 + -15x + x2 = 0 + 45000
-15x + x2 = 0 + 45000
Combine like terms: 0 + 45000 = 45000
-15x + x2 = 45000
The x term is -15x. Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.
Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 45000 + 56.25
Reorder the terms:
56.25 + -15x + x2 = 45000 + 56.25
Combine like terms: 45000 + 56.25 = 45056.25
56.25 + -15x + x2 = 45056.25
Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 45056.25
Calculate the square root of the right side: 212.264575471
Break this problem into two subproblems by setting
(x + -7.5) equal to 212.264575471 and -212.264575471.
Subproblem 1
x + -7.5 = 212.264575471
Simplifying
x + -7.5 = 212.264575471
Reorder the terms:
-7.5 + x = 212.264575471
Solving
-7.5 + x = 212.264575471
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 212.264575471 + 7.5
Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 212.264575471 + 7.5
x = 212.264575471 + 7.5
Combine like terms: 212.264575471 + 7.5 = 219.764575471
x = 219.764575471
Simplifying
x = 219.764575471
Subproblem 2
x + -7.5 = -212.264575471
Simplifying
x + -7.5 = -212.264575471
Reorder the terms:
-7.5 + x = -212.264575471
Solving
-7.5 + x = -212.264575471
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -212.264575471 + 7.5
Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -212.264575471 + 7.5
x = -212.264575471 + 7.5
Combine like terms: -212.264575471 + 7.5 = -204.764575471
x = -204.764575471
Simplifying
x = -204.764575471
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {219.764575471, -204.764575471}