x^2+64x+1024=1000

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Solution for x^2+64x+1024=1000 equation:


Simplifying
x2 + 64x + 1024 = 1000

Reorder the terms:
1024 + 64x + x2 = 1000

Solving
1024 + 64x + x2 = 1000

Solving for variable 'x'.

Reorder the terms:
1024 + -1000 + 64x + x2 = 1000 + -1000

Combine like terms: 1024 + -1000 = 24
24 + 64x + x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
24 + 64x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + 64x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + 64x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 64x + x2 = 0 + -24
64x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
64x + x2 = -24

The x term is 64x.  Take half its coefficient (32).
Square it (1024) and add it to both sides.

Add '1024' to each side of the equation.
64x + 1024 + x2 = -24 + 1024

Reorder the terms:
1024 + 64x + x2 = -24 + 1024

Combine like terms: -24 + 1024 = 1000
1024 + 64x + x2 = 1000

Factor a perfect square on the left side:
(x + 32)(x + 32) = 1000

Calculate the square root of the right side: 31.622776602

Break this problem into two subproblems by setting 
(x + 32) equal to 31.622776602 and -31.622776602.

Subproblem 1

x + 32 = 31.622776602 Simplifying x + 32 = 31.622776602 Reorder the terms: 32 + x = 31.622776602 Solving 32 + x = 31.622776602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = 31.622776602 + -32 Combine like terms: 32 + -32 = 0 0 + x = 31.622776602 + -32 x = 31.622776602 + -32 Combine like terms: 31.622776602 + -32 = -0.377223398 x = -0.377223398 Simplifying x = -0.377223398

Subproblem 2

x + 32 = -31.622776602 Simplifying x + 32 = -31.622776602 Reorder the terms: 32 + x = -31.622776602 Solving 32 + x = -31.622776602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = -31.622776602 + -32 Combine like terms: 32 + -32 = 0 0 + x = -31.622776602 + -32 x = -31.622776602 + -32 Combine like terms: -31.622776602 + -32 = -63.622776602 x = -63.622776602 Simplifying x = -63.622776602

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.377223398, -63.622776602}

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