4x+70=x^2-2x+26

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Solution for 4x+70=x^2-2x+26 equation:


Simplifying
4x + 70 = x2 + -2x + 26

Reorder the terms:
70 + 4x = x2 + -2x + 26

Reorder the terms:
70 + 4x = 26 + -2x + x2

Solving
70 + 4x = 26 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
70 + -26 + 4x + 2x + -1x2 = 26 + -2x + x2 + -26 + 2x + -1x2

Combine like terms: 70 + -26 = 44
44 + 4x + 2x + -1x2 = 26 + -2x + x2 + -26 + 2x + -1x2

Combine like terms: 4x + 2x = 6x
44 + 6x + -1x2 = 26 + -2x + x2 + -26 + 2x + -1x2

Reorder the terms:
44 + 6x + -1x2 = 26 + -26 + -2x + 2x + x2 + -1x2

Combine like terms: 26 + -26 = 0
44 + 6x + -1x2 = 0 + -2x + 2x + x2 + -1x2
44 + 6x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
44 + 6x + -1x2 = 0 + x2 + -1x2
44 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
44 + 6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-44 + -6x + x2 = 0

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -6x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + -6x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + -6x + x2 = 0 + 44
-6x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
-6x + x2 = 44

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 44 + 9

Reorder the terms:
9 + -6x + x2 = 44 + 9

Combine like terms: 44 + 9 = 53
9 + -6x + x2 = 53

Factor a perfect square on the left side:
(x + -3)(x + -3) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(x + -3) equal to 7.280109889 and -7.280109889.

Subproblem 1

x + -3 = 7.280109889 Simplifying x + -3 = 7.280109889 Reorder the terms: -3 + x = 7.280109889 Solving -3 + x = 7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 7.280109889 + 3 Combine like terms: -3 + 3 = 0 0 + x = 7.280109889 + 3 x = 7.280109889 + 3 Combine like terms: 7.280109889 + 3 = 10.280109889 x = 10.280109889 Simplifying x = 10.280109889

Subproblem 2

x + -3 = -7.280109889 Simplifying x + -3 = -7.280109889 Reorder the terms: -3 + x = -7.280109889 Solving -3 + x = -7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -7.280109889 + 3 Combine like terms: -3 + 3 = 0 0 + x = -7.280109889 + 3 x = -7.280109889 + 3 Combine like terms: -7.280109889 + 3 = -4.280109889 x = -4.280109889 Simplifying x = -4.280109889

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.280109889, -4.280109889}

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