x*x+3=5*x+7

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Solution for x*x+3=5*x+7 equation:


Simplifying
x * x + 3 = 5x + 7

Multiply x * x
x2 + 3 = 5x + 7

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

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

Solving
3 + x2 = 7 + 5x

Solving for variable 'x'.

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

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

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

Combine like terms: 7 + -7 = 0
-4 + -5x + x2 = 0 + 5x + -5x
-4 + -5x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-4 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5x + x2 = 0 + 4
-5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-5x + x2 = 4

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 4 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + -5x + x2 = 10.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

x + -2.5 = 3.201562119 Simplifying x + -2.5 = 3.201562119 Reorder the terms: -2.5 + x = 3.201562119 Solving -2.5 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.201562119 + 2.5 x = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 x = 5.701562119 Simplifying x = 5.701562119

Subproblem 2

x + -2.5 = -3.201562119 Simplifying x + -2.5 = -3.201562119 Reorder the terms: -2.5 + x = -3.201562119 Solving -2.5 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.201562119 + 2.5 x = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 x = -0.701562119 Simplifying x = -0.701562119

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.701562119, -0.701562119}

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