45x^2+14x-3=0

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Solution for 45x^2+14x-3=0 equation:


Simplifying
45x2 + 14x + -3 = 0

Reorder the terms:
-3 + 14x + 45x2 = 0

Solving
-3 + 14x + 45x2 = 0

Solving for variable 'x'.

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

Divide each side by '45'.
-0.06666666667 + 0.3111111111x + x2 = 0

Move the constant term to the right:

Add '0.06666666667' to each side of the equation.
-0.06666666667 + 0.3111111111x + 0.06666666667 + x2 = 0 + 0.06666666667

Reorder the terms:
-0.06666666667 + 0.06666666667 + 0.3111111111x + x2 = 0 + 0.06666666667

Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000
0.00000000000 + 0.3111111111x + x2 = 0 + 0.06666666667
0.3111111111x + x2 = 0 + 0.06666666667

Combine like terms: 0 + 0.06666666667 = 0.06666666667
0.3111111111x + x2 = 0.06666666667

The x term is 0.3111111111x.  Take half its coefficient (0.1555555556).
Square it (0.02419753088) and add it to both sides.

Add '0.02419753088' to each side of the equation.
0.3111111111x + 0.02419753088 + x2 = 0.06666666667 + 0.02419753088

Reorder the terms:
0.02419753088 + 0.3111111111x + x2 = 0.06666666667 + 0.02419753088

Combine like terms: 0.06666666667 + 0.02419753088 = 0.09086419755
0.02419753088 + 0.3111111111x + x2 = 0.09086419755

Factor a perfect square on the left side:
(x + 0.1555555556)(x + 0.1555555556) = 0.09086419755

Calculate the square root of the right side: 0.301436888

Break this problem into two subproblems by setting 
(x + 0.1555555556) equal to 0.301436888 and -0.301436888.

Subproblem 1

x + 0.1555555556 = 0.301436888 Simplifying x + 0.1555555556 = 0.301436888 Reorder the terms: 0.1555555556 + x = 0.301436888 Solving 0.1555555556 + x = 0.301436888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1555555556' to each side of the equation. 0.1555555556 + -0.1555555556 + x = 0.301436888 + -0.1555555556 Combine like terms: 0.1555555556 + -0.1555555556 = 0.0000000000 0.0000000000 + x = 0.301436888 + -0.1555555556 x = 0.301436888 + -0.1555555556 Combine like terms: 0.301436888 + -0.1555555556 = 0.1458813324 x = 0.1458813324 Simplifying x = 0.1458813324

Subproblem 2

x + 0.1555555556 = -0.301436888 Simplifying x + 0.1555555556 = -0.301436888 Reorder the terms: 0.1555555556 + x = -0.301436888 Solving 0.1555555556 + x = -0.301436888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1555555556' to each side of the equation. 0.1555555556 + -0.1555555556 + x = -0.301436888 + -0.1555555556 Combine like terms: 0.1555555556 + -0.1555555556 = 0.0000000000 0.0000000000 + x = -0.301436888 + -0.1555555556 x = -0.301436888 + -0.1555555556 Combine like terms: -0.301436888 + -0.1555555556 = -0.4569924436 x = -0.4569924436 Simplifying x = -0.4569924436

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1458813324, -0.4569924436}

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