please solve
x² - 10x - 32
Answers
Answer:
x = {2.549834435, -12.549834435}
Step-by-step explanation:
Simplifying
x2 + 10x + -32 = 0
Reorder the terms:
-32 + 10x + x2 = 0
Solving
-32 + 10x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '32' to each side of the equation.
-32 + 10x + 32 + x2 = 0 + 32
Reorder the terms:
-32 + 32 + 10x + x2 = 0 + 32
Combine like terms: -32 + 32 = 0
0 + 10x + x2 = 0 + 32
10x + x2 = 0 + 32
Combine like terms: 0 + 32 = 32
10x + x2 = 32
The x term is 10x. Take half its coefficient (5).
Square it (25) and add it to both sides.
Add '25' to each side of the equation.
10x + 25 + x2 = 32 + 25
Reorder the terms:
25 + 10x + x2 = 32 + 25
Combine like terms: 32 + 25 = 57
25 + 10x + x2 = 57
Factor a perfect square on the left side:
(x + 5)(x + 5) = 57
Calculate the square root of the right side: 7.549834435
Break this problem into two subproblems by setting
(x + 5) equal to 7.549834435 and -7.549834435.
Subproblem 1
x + 5 = 7.549834435
Simplifying
x + 5 = 7.549834435
Reorder the terms:
5 + x = 7.549834435
Solving
5 + x = 7.549834435
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5' to each side of the equation.
5 + -5 + x = 7.549834435 + -5
Combine like terms: 5 + -5 = 0
0 + x = 7.549834435 + -5
x = 7.549834435 + -5
Combine like terms: 7.549834435 + -5 = 2.549834435
x = 2.549834435
Simplifying
x = 2.549834435
Subproblem 2
x + 5 = -7.549834435
Simplifying
x + 5 = -7.549834435
Reorder the terms:
5 + x = -7.549834435
Solving
5 + x = -7.549834435
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5' to each side of the equation.
5 + -5 + x = -7.549834435 + -5
Combine like terms: 5 + -5 = 0
0 + x = -7.549834435 + -5
x = -7.549834435 + -5
Combine like terms: -7.549834435 + -5 = -12.549834435
x = -12.549834435
Simplifying
x = -12.549834435
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.549834435, -12.549834435}