10x^2+9x-14=0

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Solution for 10x^2+9x-14=0 equation:


Simplifying
10x2 + 9x + -14 = 0

Reorder the terms:
-14 + 9x + 10x2 = 0

Solving
-14 + 9x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-1.4 + 0.9x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 0.9x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 0.9x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 0.9x + x2 = 0 + 1.4
0.9x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
0.9x + x2 = 1.4

The x term is 0.9x.  Take half its coefficient (0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
0.9x + 0.2025 + x2 = 1.4 + 0.2025

Reorder the terms:
0.2025 + 0.9x + x2 = 1.4 + 0.2025

Combine like terms: 1.4 + 0.2025 = 1.6025
0.2025 + 0.9x + x2 = 1.6025

Factor a perfect square on the left side:
(x + 0.45)(x + 0.45) = 1.6025

Calculate the square root of the right side: 1.26589889

Break this problem into two subproblems by setting 
(x + 0.45) equal to 1.26589889 and -1.26589889.

Subproblem 1

x + 0.45 = 1.26589889 Simplifying x + 0.45 = 1.26589889 Reorder the terms: 0.45 + x = 1.26589889 Solving 0.45 + x = 1.26589889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = 1.26589889 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 1.26589889 + -0.45 x = 1.26589889 + -0.45 Combine like terms: 1.26589889 + -0.45 = 0.81589889 x = 0.81589889 Simplifying x = 0.81589889

Subproblem 2

x + 0.45 = -1.26589889 Simplifying x + 0.45 = -1.26589889 Reorder the terms: 0.45 + x = -1.26589889 Solving 0.45 + x = -1.26589889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = -1.26589889 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -1.26589889 + -0.45 x = -1.26589889 + -0.45 Combine like terms: -1.26589889 + -0.45 = -1.71589889 x = -1.71589889 Simplifying x = -1.71589889

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.81589889, -1.71589889}

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