x^2-1033x+5742=0

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Solution for x^2-1033x+5742=0 equation:


Simplifying
x2 + -1033x + 5742 = 0

Reorder the terms:
5742 + -1033x + x2 = 0

Solving
5742 + -1033x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5742' to each side of the equation.
5742 + -1033x + -5742 + x2 = 0 + -5742

Reorder the terms:
5742 + -5742 + -1033x + x2 = 0 + -5742

Combine like terms: 5742 + -5742 = 0
0 + -1033x + x2 = 0 + -5742
-1033x + x2 = 0 + -5742

Combine like terms: 0 + -5742 = -5742
-1033x + x2 = -5742

The x term is -1033x.  Take half its coefficient (-516.5).
Square it (266772.25) and add it to both sides.

Add '266772.25' to each side of the equation.
-1033x + 266772.25 + x2 = -5742 + 266772.25

Reorder the terms:
266772.25 + -1033x + x2 = -5742 + 266772.25

Combine like terms: -5742 + 266772.25 = 261030.25
266772.25 + -1033x + x2 = 261030.25

Factor a perfect square on the left side:
(x + -516.5)(x + -516.5) = 261030.25

Calculate the square root of the right side: 510.911195806

Break this problem into two subproblems by setting 
(x + -516.5) equal to 510.911195806 and -510.911195806.

Subproblem 1

x + -516.5 = 510.911195806 Simplifying x + -516.5 = 510.911195806 Reorder the terms: -516.5 + x = 510.911195806 Solving -516.5 + x = 510.911195806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '516.5' to each side of the equation. -516.5 + 516.5 + x = 510.911195806 + 516.5 Combine like terms: -516.5 + 516.5 = 0.0 0.0 + x = 510.911195806 + 516.5 x = 510.911195806 + 516.5 Combine like terms: 510.911195806 + 516.5 = 1027.411195806 x = 1027.411195806 Simplifying x = 1027.411195806

Subproblem 2

x + -516.5 = -510.911195806 Simplifying x + -516.5 = -510.911195806 Reorder the terms: -516.5 + x = -510.911195806 Solving -516.5 + x = -510.911195806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '516.5' to each side of the equation. -516.5 + 516.5 + x = -510.911195806 + 516.5 Combine like terms: -516.5 + 516.5 = 0.0 0.0 + x = -510.911195806 + 516.5 x = -510.911195806 + 516.5 Combine like terms: -510.911195806 + 516.5 = 5.588804194 x = 5.588804194 Simplifying x = 5.588804194

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1027.411195806, 5.588804194}

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