2x^2+5x-3=14

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Solution for 2x^2+5x-3=14 equation:


Simplifying
2x2 + 5x + -3 = 14

Reorder the terms:
-3 + 5x + 2x2 = 14

Solving
-3 + 5x + 2x2 = 14

Solving for variable 'x'.

Reorder the terms:
-3 + -14 + 5x + 2x2 = 14 + -14

Combine like terms: -3 + -14 = -17
-17 + 5x + 2x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-17 + 5x + 2x2 = 0

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

Divide each side by '2'.
-8.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 2.5x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 2.5x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 2.5x + x2 = 0 + 8.5
2.5x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
2.5x + x2 = 8.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 8.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 8.5 + 1.5625

Combine like terms: 8.5 + 1.5625 = 10.0625
1.5625 + 2.5x + x2 = 10.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 10.0625

Calculate the square root of the right side: 3.172144385

Break this problem into two subproblems by setting 
(x + 1.25) equal to 3.172144385 and -3.172144385.

Subproblem 1

x + 1.25 = 3.172144385 Simplifying x + 1.25 = 3.172144385 Reorder the terms: 1.25 + x = 3.172144385 Solving 1.25 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 3.172144385 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.172144385 + -1.25 x = 3.172144385 + -1.25 Combine like terms: 3.172144385 + -1.25 = 1.922144385 x = 1.922144385 Simplifying x = 1.922144385

Subproblem 2

x + 1.25 = -3.172144385 Simplifying x + 1.25 = -3.172144385 Reorder the terms: 1.25 + x = -3.172144385 Solving 1.25 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -3.172144385 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.172144385 + -1.25 x = -3.172144385 + -1.25 Combine like terms: -3.172144385 + -1.25 = -4.422144385 x = -4.422144385 Simplifying x = -4.422144385

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.922144385, -4.422144385}

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