-2x^2-7x+5=0

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Solution for -2x^2-7x+5=0 equation:


Simplifying
-2x2 + -7x + 5 = 0

Reorder the terms:
5 + -7x + -2x2 = 0

Solving
5 + -7x + -2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-2.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 3.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 3.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 3.5x + x2 = 0 + 2.5
3.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
3.5x + x2 = 2.5

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 2.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 2.5 + 3.0625

Combine like terms: 2.5 + 3.0625 = 5.5625
3.0625 + 3.5x + x2 = 5.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(x + 1.75) equal to 2.358495283 and -2.358495283.

Subproblem 1

x + 1.75 = 2.358495283 Simplifying x + 1.75 = 2.358495283 Reorder the terms: 1.75 + x = 2.358495283 Solving 1.75 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 2.358495283 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.358495283 + -1.75 x = 2.358495283 + -1.75 Combine like terms: 2.358495283 + -1.75 = 0.608495283 x = 0.608495283 Simplifying x = 0.608495283

Subproblem 2

x + 1.75 = -2.358495283 Simplifying x + 1.75 = -2.358495283 Reorder the terms: 1.75 + x = -2.358495283 Solving 1.75 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -2.358495283 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.358495283 + -1.75 x = -2.358495283 + -1.75 Combine like terms: -2.358495283 + -1.75 = -4.108495283 x = -4.108495283 Simplifying x = -4.108495283

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.608495283, -4.108495283}

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