x^2+7x-5=3x+4

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Solution for x^2+7x-5=3x+4 equation:


Simplifying
x2 + 7x + -5 = 3x + 4

Reorder the terms:
-5 + 7x + x2 = 3x + 4

Reorder the terms:
-5 + 7x + x2 = 4 + 3x

Solving
-5 + 7x + x2 = 4 + 3x

Solving for variable 'x'.

Reorder the terms:
-5 + -4 + 7x + -3x + x2 = 4 + 3x + -4 + -3x

Combine like terms: -5 + -4 = -9
-9 + 7x + -3x + x2 = 4 + 3x + -4 + -3x

Combine like terms: 7x + -3x = 4x
-9 + 4x + x2 = 4 + 3x + -4 + -3x

Reorder the terms:
-9 + 4x + x2 = 4 + -4 + 3x + -3x

Combine like terms: 4 + -4 = 0
-9 + 4x + x2 = 0 + 3x + -3x
-9 + 4x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-9 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 4x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 4x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 4x + x2 = 0 + 9
4x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
4x + x2 = 9

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 9 + 4

Reorder the terms:
4 + 4x + x2 = 9 + 4

Combine like terms: 9 + 4 = 13
4 + 4x + x2 = 13

Factor a perfect square on the left side:
(x + 2)(x + 2) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 2) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + 2 = 3.605551275 Simplifying x + 2 = 3.605551275 Reorder the terms: 2 + x = 3.605551275 Solving 2 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.605551275 + -2 x = 3.605551275 + -2 Combine like terms: 3.605551275 + -2 = 1.605551275 x = 1.605551275 Simplifying x = 1.605551275

Subproblem 2

x + 2 = -3.605551275 Simplifying x + 2 = -3.605551275 Reorder the terms: 2 + x = -3.605551275 Solving 2 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.605551275 + -2 x = -3.605551275 + -2 Combine like terms: -3.605551275 + -2 = -5.605551275 x = -5.605551275 Simplifying x = -5.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.605551275, -5.605551275}

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