x^2+.7x=.51

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Solution for x^2+.7x=.51 equation:


Simplifying
x2 + 0.7x = 0.51

Reorder the terms:
0.7x + x2 = 0.51

Solving
0.7x + x2 = 0.51

Solving for variable 'x'.

Reorder the terms:
-0.51 + 0.7x + x2 = 0.51 + -0.51

Combine like terms: 0.51 + -0.51 = 0.00
-0.51 + 0.7x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.51' to each side of the equation.
-0.51 + 0.7x + 0.51 + x2 = 0.00 + 0.51

Reorder the terms:
-0.51 + 0.51 + 0.7x + x2 = 0.00 + 0.51

Combine like terms: -0.51 + 0.51 = 0.00
0.00 + 0.7x + x2 = 0.00 + 0.51
0.7x + x2 = 0.00 + 0.51

Combine like terms: 0.00 + 0.51 = 0.51
0.7x + x2 = 0.51

The x term is 0.7x.  Take half its coefficient (0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
0.7x + 0.1225 + x2 = 0.51 + 0.1225

Reorder the terms:
0.1225 + 0.7x + x2 = 0.51 + 0.1225

Combine like terms: 0.51 + 0.1225 = 0.6325
0.1225 + 0.7x + x2 = 0.6325

Factor a perfect square on the left side:
(x + 0.35)(x + 0.35) = 0.6325

Calculate the square root of the right side: 0.795298686

Break this problem into two subproblems by setting 
(x + 0.35) equal to 0.795298686 and -0.795298686.

Subproblem 1

x + 0.35 = 0.795298686 Simplifying x + 0.35 = 0.795298686 Reorder the terms: 0.35 + x = 0.795298686 Solving 0.35 + x = 0.795298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 0.795298686 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 0.795298686 + -0.35 x = 0.795298686 + -0.35 Combine like terms: 0.795298686 + -0.35 = 0.445298686 x = 0.445298686 Simplifying x = 0.445298686

Subproblem 2

x + 0.35 = -0.795298686 Simplifying x + 0.35 = -0.795298686 Reorder the terms: 0.35 + x = -0.795298686 Solving 0.35 + x = -0.795298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -0.795298686 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -0.795298686 + -0.35 x = -0.795298686 + -0.35 Combine like terms: -0.795298686 + -0.35 = -1.145298686 x = -1.145298686 Simplifying x = -1.145298686

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.445298686, -1.145298686}

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