x^2+10x+21=1156

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Solution for x^2+10x+21=1156 equation:


Simplifying
x2 + 10x + 21 = 1156

Reorder the terms:
21 + 10x + x2 = 1156

Solving
21 + 10x + x2 = 1156

Solving for variable 'x'.

Reorder the terms:
21 + -1156 + 10x + x2 = 1156 + -1156

Combine like terms: 21 + -1156 = -1135
-1135 + 10x + x2 = 1156 + -1156

Combine like terms: 1156 + -1156 = 0
-1135 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1135' to each side of the equation.
-1135 + 10x + 1135 + x2 = 0 + 1135

Reorder the terms:
-1135 + 1135 + 10x + x2 = 0 + 1135

Combine like terms: -1135 + 1135 = 0
0 + 10x + x2 = 0 + 1135
10x + x2 = 0 + 1135

Combine like terms: 0 + 1135 = 1135
10x + x2 = 1135

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 1135 + 25

Reorder the terms:
25 + 10x + x2 = 1135 + 25

Combine like terms: 1135 + 25 = 1160
25 + 10x + x2 = 1160

Factor a perfect square on the left side:
(x + 5)(x + 5) = 1160

Calculate the square root of the right side: 34.058772732

Break this problem into two subproblems by setting 
(x + 5) equal to 34.058772732 and -34.058772732.

Subproblem 1

x + 5 = 34.058772732 Simplifying x + 5 = 34.058772732 Reorder the terms: 5 + x = 34.058772732 Solving 5 + x = 34.058772732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 34.058772732 + -5 Combine like terms: 5 + -5 = 0 0 + x = 34.058772732 + -5 x = 34.058772732 + -5 Combine like terms: 34.058772732 + -5 = 29.058772732 x = 29.058772732 Simplifying x = 29.058772732

Subproblem 2

x + 5 = -34.058772732 Simplifying x + 5 = -34.058772732 Reorder the terms: 5 + x = -34.058772732 Solving 5 + x = -34.058772732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -34.058772732 + -5 Combine like terms: 5 + -5 = 0 0 + x = -34.058772732 + -5 x = -34.058772732 + -5 Combine like terms: -34.058772732 + -5 = -39.058772732 x = -39.058772732 Simplifying x = -39.058772732

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.058772732, -39.058772732}

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