Factorise 5x^2 -28x + 39.2
Answers
Answer:
Simplifying
5x2 + 4x = 196
Reorder the terms:
4x + 5x2 = 196
Solving
4x + 5x2 = 196
Solving for variable 'x'.
Reorder the terms:
-196 + 4x + 5x2 = 196 + -196
Combine like terms: 196 + -196 = 0
-196 + 4x + 5x2 = 0
Begin completing the square. Divide all terms by
5 the coefficient of the squared term:
Divide each side by '5'.
-39.2 + 0.8x + x2 = 0
Move the constant term to the right:
Add '39.2' to each side of the equation.
-39.2 + 0.8x + 39.2 + x2 = 0 + 39.2
Reorder the terms:
-39.2 + 39.2 + 0.8x + x2 = 0 + 39.2
Combine like terms: -39.2 + 39.2 = 0.0
0.0 + 0.8x + x2 = 0 + 39.2
0.8x + x2 = 0 + 39.2
Combine like terms: 0 + 39.2 = 39.2
0.8x + x2 = 39.2
The x term is 0.8x. Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.
Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 39.2 + 0.16
Reorder the terms:
0.16 + 0.8x + x2 = 39.2 + 0.16
Combine like terms: 39.2 + 0.16 = 39.36
0.16 + 0.8x + x2 = 39.36
Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 39.36
Calculate the square root of the right side: 6.273754857
Break this problem into two subproblems by setting
(x + 0.4) equal to 6.273754857 and -6.273754857.
Subproblem 1
x + 0.4 = 6.273754857
Simplifying
x + 0.4 = 6.273754857
Reorder the terms:
0.4 + x = 6.273754857
Solving
0.4 + x = 6.273754857
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 6.273754857 + -0.4
Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 6.273754857 + -0.4
x = 6.273754857 + -0.4
Combine like terms: 6.273754857 + -0.4 = 5.873754857
x = 5.873754857
Simplifying
x = 5.873754857
Subproblem 2
x + 0.4 = -6.273754857
Simplifying
x + 0.4 = -6.273754857
Reorder the terms:
0.4 + x = -6.273754857
Solving
0.4 + x = -6.273754857
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -6.273754857 + -0.4
Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -6.273754857 + -0.4
x = -6.273754857 + -0.4
Combine like terms: -6.273754857 + -0.4 = -6.673754857
x = -6.673754857
Simplifying
x = -6.673754857
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.873754857, -6.673754857}