x^2-13x+30=4

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Solution for x^2-13x+30=4 equation:


Simplifying
x2 + -13x + 30 = 4

Reorder the terms:
30 + -13x + x2 = 4

Solving
30 + -13x + x2 = 4

Solving for variable 'x'.

Reorder the terms:
30 + -4 + -13x + x2 = 4 + -4

Combine like terms: 30 + -4 = 26
26 + -13x + x2 = 4 + -4

Combine like terms: 4 + -4 = 0
26 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + -13x + -26 + x2 = 0 + -26

Reorder the terms:
26 + -26 + -13x + x2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -13x + x2 = 0 + -26
-13x + x2 = 0 + -26

Combine like terms: 0 + -26 = -26
-13x + x2 = -26

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -26 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -26 + 42.25

Combine like terms: -26 + 42.25 = 16.25
42.25 + -13x + x2 = 16.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + -6.5) equal to 4.031128874 and -4.031128874.

Subproblem 1

x + -6.5 = 4.031128874 Simplifying x + -6.5 = 4.031128874 Reorder the terms: -6.5 + x = 4.031128874 Solving -6.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 4.031128874 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 4.031128874 + 6.5 x = 4.031128874 + 6.5 Combine like terms: 4.031128874 + 6.5 = 10.531128874 x = 10.531128874 Simplifying x = 10.531128874

Subproblem 2

x + -6.5 = -4.031128874 Simplifying x + -6.5 = -4.031128874 Reorder the terms: -6.5 + x = -4.031128874 Solving -6.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -4.031128874 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -4.031128874 + 6.5 x = -4.031128874 + 6.5 Combine like terms: -4.031128874 + 6.5 = 2.468871126 x = 2.468871126 Simplifying x = 2.468871126

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.531128874, 2.468871126}

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