x^2+3x+4=1056

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Solution for x^2+3x+4=1056 equation:


Simplifying
x2 + 3x + 4 = 1056

Reorder the terms:
4 + 3x + x2 = 1056

Solving
4 + 3x + x2 = 1056

Solving for variable 'x'.

Reorder the terms:
4 + -1056 + 3x + x2 = 1056 + -1056

Combine like terms: 4 + -1056 = -1052
-1052 + 3x + x2 = 1056 + -1056

Combine like terms: 1056 + -1056 = 0
-1052 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1052' to each side of the equation.
-1052 + 3x + 1052 + x2 = 0 + 1052

Reorder the terms:
-1052 + 1052 + 3x + x2 = 0 + 1052

Combine like terms: -1052 + 1052 = 0
0 + 3x + x2 = 0 + 1052
3x + x2 = 0 + 1052

Combine like terms: 0 + 1052 = 1052
3x + x2 = 1052

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 1052 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1052 + 2.25

Combine like terms: 1052 + 2.25 = 1054.25
2.25 + 3x + x2 = 1054.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 1054.25

Calculate the square root of the right side: 32.46921619

Break this problem into two subproblems by setting 
(x + 1.5) equal to 32.46921619 and -32.46921619.

Subproblem 1

x + 1.5 = 32.46921619 Simplifying x + 1.5 = 32.46921619 Reorder the terms: 1.5 + x = 32.46921619 Solving 1.5 + x = 32.46921619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 32.46921619 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 32.46921619 + -1.5 x = 32.46921619 + -1.5 Combine like terms: 32.46921619 + -1.5 = 30.96921619 x = 30.96921619 Simplifying x = 30.96921619

Subproblem 2

x + 1.5 = -32.46921619 Simplifying x + 1.5 = -32.46921619 Reorder the terms: 1.5 + x = -32.46921619 Solving 1.5 + x = -32.46921619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -32.46921619 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -32.46921619 + -1.5 x = -32.46921619 + -1.5 Combine like terms: -32.46921619 + -1.5 = -33.96921619 x = -33.96921619 Simplifying x = -33.96921619

Solution

The solution to the problem is based on the solutions from the subproblems. x = {30.96921619, -33.96921619}

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