find the value of X X2+3X-30=0
Answers
Answer:
Step-by-step explanation:
- First simplifying,
x^2 + 3x - 30 = 0
- Next reorder the terms,
-30 + 3x + x^2 = 0
- Solving for variable 'x'
-30 + 3x + x^2 = 0
- Begin completing the square.
Move the constant term to the right:
- Add '30' to each side of the equation.
-30 + 3x + 30 + x^2 = 0 + 30
- Reorder the terms:
-30 + 30 + 3x + x^2 = 0 + 30
- Combine like terms: -30 + 30 = 0
0 + 3x + x^2 = 0 + 30
3x + x^2 = 0 + 30
- Combine like terms: 0 + 30 = 30
3x + x^2 = 30
- The x term is 3x. Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.
- Add '2.25' to each side of the equation.
3x + 2.25 + x^2 = 30 + 2.25
- Reorder the terms:
2.25 + 3x + x^2 = 30 + 2.25
- Combine like terms: 30 + 2.25 = 32.25
2.25 + 3x + x^2 = 32.25
- Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 32.25
- Calculate the square root of the right side: 5.678908346
- Break this problem into two subproblems by setting
(x + 1.5) equal to 5.678908346 and -5.678908346.
Case 1
x + 1.5 = 5.678908346
- Simplifying
x + 1.5 = 5.678908346
- Reorder the terms:
1.5 + x = 5.678908346
- Solving for variable 'x'.
1.5 + x = 5.678908346
- Move all terms containing x to the left, all other terms to the right.
- Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 5.678908346 + -1.5
- Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 5.678908346 + -1.5
x = 5.678908346 + -1.5
- Combine like terms: 5.678908346 + -1.5 = 4.178908346
x = 4.178908346
- Simplifying
x = 4.178908346
Case 2
x + 1.5 = -5.678908346
- Simplifying
x + 1.5 = -5.678908346
- Reorder the terms:
1.5 + x = -5.678908346
- Solving for variable 'x'.
1.5 + x = -5.678908346
- Move all terms containing x to the left, all other terms to the right.
- Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -5.678908346 + -1.5
- Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -5.678908346 + -1.5
x = -5.678908346 + -1.5
- Combine like terms: -5.678908346 + -1.5 = -7.178908346
x = -7.178908346
- Simplifying
x = -7.178908346
Solution
The solution to the problem is based on the solutions
from the two cases,
x = {4.178908346, -7.178908346}
Thank me if u got it
Mark me as the brainliest :)