2x^2+2x-75 factorise
Answers
Simplifying
2x2 + 2x + -75 = 0
Reorder the terms:
-75 + 2x + 2x2 = 0
Solving
-75 + 2x + 2x2 = 0
Solving for variable 'x'.
Begin completing the square. Divide all terms by
2 the coefficient of the squared term:
Divide each side by '2'.
-37.5 + x + x2 = 0
Move the constant term to the right:
Add '37.5' to each side of the equation.
-37.5 + x + 37.5 + x2 = 0 + 37.5
Reorder the terms:
-37.5 + 37.5 + x + x2 = 0 + 37.5
Combine like terms: -37.5 + 37.5 = 0.0
0.0 + x + x2 = 0 + 37.5
x + x2 = 0 + 37.5
Combine like terms: 0 + 37.5 = 37.5
x + x2 = 37.5
The x term is x. Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.
Add '0.25' to each side of the equation.
+ 0.25 + x2 = 37.5 + 0.25
Combine like terms: + 0.25 = 1.25
1.25 + x2 = 37.5 + 0.25
Combine like terms: 37.5 + 0.25 = 37.75
1.25 + x2 = 37.75
Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 37.75
Calculate the square root of the right side: 6.144102864
Break this problem into two subproblems by setting
(x + 0.5) equal to 6.144102864 and -6.144102864.
Subproblem 1
x + 0.5 = 6.144102864
Simplifying
x + 0.5 = 6.144102864
Reorder the terms:
0.5 + x = 6.144102864
Solving
0.5 + x = 6.144102864
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 6.144102864 + -0.5
Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 6.144102864 + -0.5
x = 6.144102864 + -0.5
Combine like terms: 6.144102864 + -0.5 = 5.644102864
x = 5.644102864
Simplifying
x = 5.644102864
Subproblem 2
x + 0.5 = -6.144102864
Simplifying
x + 0.5 = -6.144102864
Reorder the terms:
0.5 + x = -6.144102864
Solving
0.5 + x = -6.144102864
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -6.144102864 + -0.5
Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -6.144102864 + -0.5
x = -6.144102864 + -0.5
Combine like terms: - 6.144102864 + -0.5 = -6.644102864
x = -6.644102864
Simplifying
x = -6.644102864
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.644102864, -6.644102864}
Step-by-step explanation:
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