x^2+17x-70=0

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Solution for x^2+17x-70=0 equation:


Simplifying
x2 + 17x + -70 = 0

Reorder the terms:
-70 + 17x + x2 = 0

Solving
-70 + 17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 17x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 17x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 17x + x2 = 0 + 70
17x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
17x + x2 = 70

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = 70 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 70 + 72.25

Combine like terms: 70 + 72.25 = 142.25
72.25 + 17x + x2 = 142.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 142.25

Calculate the square root of the right side: 11.926860442

Break this problem into two subproblems by setting 
(x + 8.5) equal to 11.926860442 and -11.926860442.

Subproblem 1

x + 8.5 = 11.926860442 Simplifying x + 8.5 = 11.926860442 Reorder the terms: 8.5 + x = 11.926860442 Solving 8.5 + x = 11.926860442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 11.926860442 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 11.926860442 + -8.5 x = 11.926860442 + -8.5 Combine like terms: 11.926860442 + -8.5 = 3.426860442 x = 3.426860442 Simplifying x = 3.426860442

Subproblem 2

x + 8.5 = -11.926860442 Simplifying x + 8.5 = -11.926860442 Reorder the terms: 8.5 + x = -11.926860442 Solving 8.5 + x = -11.926860442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -11.926860442 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -11.926860442 + -8.5 x = -11.926860442 + -8.5 Combine like terms: -11.926860442 + -8.5 = -20.426860442 x = -20.426860442 Simplifying x = -20.426860442

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.426860442, -20.426860442}

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