x^2+7x-.75=0

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Solution for x^2+7x-.75=0 equation:


Simplifying
x2 + 7x + -0.75 = 0

Reorder the terms:
-0.75 + 7x + x2 = 0

Solving
-0.75 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 7x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 7x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 7x + x2 = 0 + 0.75
7x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
7x + x2 = 0.75

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 0.75 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 0.75 + 12.25

Combine like terms: 0.75 + 12.25 = 13
12.25 + 7x + x2 = 13

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + 3.5 = 3.605551275 Simplifying x + 3.5 = 3.605551275 Reorder the terms: 3.5 + x = 3.605551275 Solving 3.5 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.605551275 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.605551275 + -3.5 x = 3.605551275 + -3.5 Combine like terms: 3.605551275 + -3.5 = 0.105551275 x = 0.105551275 Simplifying x = 0.105551275

Subproblem 2

x + 3.5 = -3.605551275 Simplifying x + 3.5 = -3.605551275 Reorder the terms: 3.5 + x = -3.605551275 Solving 3.5 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.605551275 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.605551275 + -3.5 x = -3.605551275 + -3.5 Combine like terms: -3.605551275 + -3.5 = -7.105551275 x = -7.105551275 Simplifying x = -7.105551275

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.105551275, -7.105551275}

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