x^2-20x+13=(-63)

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Solution for x^2-20x+13=(-63) equation:


Simplifying
x2 + -20x + 13 = (-63)

Reorder the terms:
13 + -20x + x2 = (-63)
13 + -20x + x2 = -63

Solving
13 + -20x + x2 = -63

Solving for variable 'x'.

Reorder the terms:
13 + 63 + -20x + x2 = -63 + 63

Combine like terms: 13 + 63 = 76
76 + -20x + x2 = -63 + 63

Combine like terms: -63 + 63 = 0
76 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-76' to each side of the equation.
76 + -20x + -76 + x2 = 0 + -76

Reorder the terms:
76 + -76 + -20x + x2 = 0 + -76

Combine like terms: 76 + -76 = 0
0 + -20x + x2 = 0 + -76
-20x + x2 = 0 + -76

Combine like terms: 0 + -76 = -76
-20x + x2 = -76

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -76 + 100

Reorder the terms:
100 + -20x + x2 = -76 + 100

Combine like terms: -76 + 100 = 24
100 + -20x + x2 = 24

Factor a perfect square on the left side:
(x + -10)(x + -10) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -10) equal to 4.898979486 and -4.898979486.

Subproblem 1

x + -10 = 4.898979486 Simplifying x + -10 = 4.898979486 Reorder the terms: -10 + x = 4.898979486 Solving -10 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 4.898979486 + 10 Combine like terms: -10 + 10 = 0 0 + x = 4.898979486 + 10 x = 4.898979486 + 10 Combine like terms: 4.898979486 + 10 = 14.898979486 x = 14.898979486 Simplifying x = 14.898979486

Subproblem 2

x + -10 = -4.898979486 Simplifying x + -10 = -4.898979486 Reorder the terms: -10 + x = -4.898979486 Solving -10 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -4.898979486 + 10 Combine like terms: -10 + 10 = 0 0 + x = -4.898979486 + 10 x = -4.898979486 + 10 Combine like terms: -4.898979486 + 10 = 5.101020514 x = 5.101020514 Simplifying x = 5.101020514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.898979486, 5.101020514}

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