5x^2-5.2x-2.52=0

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Solution for 5x^2-5.2x-2.52=0 equation:


Simplifying
5x2 + -5.2x + -2.52 = 0

Reorder the terms:
-2.52 + -5.2x + 5x2 = 0

Solving
-2.52 + -5.2x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-0.504 + -1.04x + x2 = 0

Move the constant term to the right:

Add '0.504' to each side of the equation.
-0.504 + -1.04x + 0.504 + x2 = 0 + 0.504

Reorder the terms:
-0.504 + 0.504 + -1.04x + x2 = 0 + 0.504

Combine like terms: -0.504 + 0.504 = 0.000
0.000 + -1.04x + x2 = 0 + 0.504
-1.04x + x2 = 0 + 0.504

Combine like terms: 0 + 0.504 = 0.504
-1.04x + x2 = 0.504

The x term is -1.04x.  Take half its coefficient (-0.52).
Square it (0.2704) and add it to both sides.

Add '0.2704' to each side of the equation.
-1.04x + 0.2704 + x2 = 0.504 + 0.2704

Reorder the terms:
0.2704 + -1.04x + x2 = 0.504 + 0.2704

Combine like terms: 0.504 + 0.2704 = 0.7744
0.2704 + -1.04x + x2 = 0.7744

Factor a perfect square on the left side:
(x + -0.52)(x + -0.52) = 0.7744

Calculate the square root of the right side: 0.88

Break this problem into two subproblems by setting 
(x + -0.52) equal to 0.88 and -0.88.

Subproblem 1

x + -0.52 = 0.88 Simplifying x + -0.52 = 0.88 Reorder the terms: -0.52 + x = 0.88 Solving -0.52 + x = 0.88 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.52' to each side of the equation. -0.52 + 0.52 + x = 0.88 + 0.52 Combine like terms: -0.52 + 0.52 = 0.00 0.00 + x = 0.88 + 0.52 x = 0.88 + 0.52 Combine like terms: 0.88 + 0.52 = 1.4 x = 1.4 Simplifying x = 1.4

Subproblem 2

x + -0.52 = -0.88 Simplifying x + -0.52 = -0.88 Reorder the terms: -0.52 + x = -0.88 Solving -0.52 + x = -0.88 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.52' to each side of the equation. -0.52 + 0.52 + x = -0.88 + 0.52 Combine like terms: -0.52 + 0.52 = 0.00 0.00 + x = -0.88 + 0.52 x = -0.88 + 0.52 Combine like terms: -0.88 + 0.52 = -0.36 x = -0.36 Simplifying x = -0.36

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.4, -0.36}

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