15-30x+14.75x^2=0

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Solution for 15-30x+14.75x^2=0 equation:


Simplifying
15 + -30x + 14.75x2 = 0

Solving
15 + -30x + 14.75x2 = 0

Solving for variable 'x'.

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

Divide each side by '14.75'.
1.016949153 + -2.033898305x + x2 = 0

Move the constant term to the right:

Add '-1.016949153' to each side of the equation.
1.016949153 + -2.033898305x + -1.016949153 + x2 = 0 + -1.016949153

Reorder the terms:
1.016949153 + -1.016949153 + -2.033898305x + x2 = 0 + -1.016949153

Combine like terms: 1.016949153 + -1.016949153 = 0.000000000
0.000000000 + -2.033898305x + x2 = 0 + -1.016949153
-2.033898305x + x2 = 0 + -1.016949153

Combine like terms: 0 + -1.016949153 = -1.016949153
-2.033898305x + x2 = -1.016949153

The x term is -2.033898305x.  Take half its coefficient (-1.016949153).
Square it (1.034185580) and add it to both sides.

Add '1.034185580' to each side of the equation.
-2.033898305x + 1.034185580 + x2 = -1.016949153 + 1.034185580

Reorder the terms:
1.034185580 + -2.033898305x + x2 = -1.016949153 + 1.034185580

Combine like terms: -1.016949153 + 1.034185580 = 0.017236427
1.034185580 + -2.033898305x + x2 = 0.017236427

Factor a perfect square on the left side:
(x + -1.016949153)(x + -1.016949153) = 0.017236427

Calculate the square root of the right side: 0.131287574

Break this problem into two subproblems by setting 
(x + -1.016949153) equal to 0.131287574 and -0.131287574.

Subproblem 1

x + -1.016949153 = 0.131287574 Simplifying x + -1.016949153 = 0.131287574 Reorder the terms: -1.016949153 + x = 0.131287574 Solving -1.016949153 + x = 0.131287574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.016949153' to each side of the equation. -1.016949153 + 1.016949153 + x = 0.131287574 + 1.016949153 Combine like terms: -1.016949153 + 1.016949153 = 0.000000000 0.000000000 + x = 0.131287574 + 1.016949153 x = 0.131287574 + 1.016949153 Combine like terms: 0.131287574 + 1.016949153 = 1.148236727 x = 1.148236727 Simplifying x = 1.148236727

Subproblem 2

x + -1.016949153 = -0.131287574 Simplifying x + -1.016949153 = -0.131287574 Reorder the terms: -1.016949153 + x = -0.131287574 Solving -1.016949153 + x = -0.131287574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.016949153' to each side of the equation. -1.016949153 + 1.016949153 + x = -0.131287574 + 1.016949153 Combine like terms: -1.016949153 + 1.016949153 = 0.000000000 0.000000000 + x = -0.131287574 + 1.016949153 x = -0.131287574 + 1.016949153 Combine like terms: -0.131287574 + 1.016949153 = 0.885661579 x = 0.885661579 Simplifying x = 0.885661579

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.148236727, 0.885661579}

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