0=x^2-4x-70

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Solution for 0=x^2-4x-70 equation:


Simplifying
0 = x2 + -4x + -70

Reorder the terms:
0 = -70 + -4x + x2

Solving
0 = -70 + -4x + x2

Solving for variable 'x'.

Combine like terms: 0 + 70 = 70
70 + 4x + -1x2 = -70 + -4x + x2 + 70 + 4x + -1x2

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

Combine like terms: -70 + 70 = 0
70 + 4x + -1x2 = 0 + -4x + 4x + x2 + -1x2
70 + 4x + -1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
70 + 4x + -1x2 = 0 + x2 + -1x2
70 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
70 + 4x + -1x2 = 0

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

Divide each side by '-1'.
-70 + -4x + x2 = 0

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + -4x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + -4x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + -4x + x2 = 0 + 70
-4x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
-4x + x2 = 70

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 70 + 4

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

Combine like terms: 70 + 4 = 74
4 + -4x + x2 = 74

Factor a perfect square on the left side:
(x + -2)(x + -2) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(x + -2) equal to 8.602325267 and -8.602325267.

Subproblem 1

x + -2 = 8.602325267 Simplifying x + -2 = 8.602325267 Reorder the terms: -2 + x = 8.602325267 Solving -2 + x = 8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 8.602325267 + 2 Combine like terms: -2 + 2 = 0 0 + x = 8.602325267 + 2 x = 8.602325267 + 2 Combine like terms: 8.602325267 + 2 = 10.602325267 x = 10.602325267 Simplifying x = 10.602325267

Subproblem 2

x + -2 = -8.602325267 Simplifying x + -2 = -8.602325267 Reorder the terms: -2 + x = -8.602325267 Solving -2 + x = -8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -8.602325267 + 2 Combine like terms: -2 + 2 = 0 0 + x = -8.602325267 + 2 x = -8.602325267 + 2 Combine like terms: -8.602325267 + 2 = -6.602325267 x = -6.602325267 Simplifying x = -6.602325267

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.602325267, -6.602325267}

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