298x^2+24x-9=0

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Solution for 298x^2+24x-9=0 equation:


Simplifying
298x2 + 24x + -9 = 0

Reorder the terms:
-9 + 24x + 298x2 = 0

Solving
-9 + 24x + 298x2 = 0

Solving for variable 'x'.

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

Divide each side by '298'.
-0.03020134228 + 0.08053691275x + x2 = 0

Move the constant term to the right:

Add '0.03020134228' to each side of the equation.
-0.03020134228 + 0.08053691275x + 0.03020134228 + x2 = 0 + 0.03020134228

Reorder the terms:
-0.03020134228 + 0.03020134228 + 0.08053691275x + x2 = 0 + 0.03020134228

Combine like terms: -0.03020134228 + 0.03020134228 = 0.00000000000
0.00000000000 + 0.08053691275x + x2 = 0 + 0.03020134228
0.08053691275x + x2 = 0 + 0.03020134228

Combine like terms: 0 + 0.03020134228 = 0.03020134228
0.08053691275x + x2 = 0.03020134228

The x term is 0.08053691275x.  Take half its coefficient (0.04026845638).
Square it (0.001621548579) and add it to both sides.

Add '0.001621548579' to each side of the equation.
0.08053691275x + 0.001621548579 + x2 = 0.03020134228 + 0.001621548579

Reorder the terms:
0.001621548579 + 0.08053691275x + x2 = 0.03020134228 + 0.001621548579

Combine like terms: 0.03020134228 + 0.001621548579 = 0.031822890859
0.001621548579 + 0.08053691275x + x2 = 0.031822890859

Factor a perfect square on the left side:
(x + 0.04026845638)(x + 0.04026845638) = 0.031822890859

Calculate the square root of the right side: 0.178389716

Break this problem into two subproblems by setting 
(x + 0.04026845638) equal to 0.178389716 and -0.178389716.

Subproblem 1

x + 0.04026845638 = 0.178389716 Simplifying x + 0.04026845638 = 0.178389716 Reorder the terms: 0.04026845638 + x = 0.178389716 Solving 0.04026845638 + x = 0.178389716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04026845638' to each side of the equation. 0.04026845638 + -0.04026845638 + x = 0.178389716 + -0.04026845638 Combine like terms: 0.04026845638 + -0.04026845638 = 0.00000000000 0.00000000000 + x = 0.178389716 + -0.04026845638 x = 0.178389716 + -0.04026845638 Combine like terms: 0.178389716 + -0.04026845638 = 0.13812125962 x = 0.13812125962 Simplifying x = 0.13812125962

Subproblem 2

x + 0.04026845638 = -0.178389716 Simplifying x + 0.04026845638 = -0.178389716 Reorder the terms: 0.04026845638 + x = -0.178389716 Solving 0.04026845638 + x = -0.178389716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04026845638' to each side of the equation. 0.04026845638 + -0.04026845638 + x = -0.178389716 + -0.04026845638 Combine like terms: 0.04026845638 + -0.04026845638 = 0.00000000000 0.00000000000 + x = -0.178389716 + -0.04026845638 x = -0.178389716 + -0.04026845638 Combine like terms: -0.178389716 + -0.04026845638 = -0.21865817238 x = -0.21865817238 Simplifying x = -0.21865817238

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.13812125962, -0.21865817238}

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