4x^2-25x+15=6

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Solution for 4x^2-25x+15=6 equation:


Simplifying
4x2 + -25x + 15 = 6

Reorder the terms:
15 + -25x + 4x2 = 6

Solving
15 + -25x + 4x2 = 6

Solving for variable 'x'.

Reorder the terms:
15 + -6 + -25x + 4x2 = 6 + -6

Combine like terms: 15 + -6 = 9
9 + -25x + 4x2 = 6 + -6

Combine like terms: 6 + -6 = 0
9 + -25x + 4x2 = 0

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

Divide each side by '4'.
2.25 + -6.25x + x2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -6.25x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -6.25x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -6.25x + x2 = 0 + -2.25
-6.25x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-6.25x + x2 = -2.25

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = -2.25 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = -2.25 + 9.765625

Combine like terms: -2.25 + 9.765625 = 7.515625
9.765625 + -6.25x + x2 = 7.515625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 7.515625

Calculate the square root of the right side: 2.741464025

Break this problem into two subproblems by setting 
(x + -3.125) equal to 2.741464025 and -2.741464025.

Subproblem 1

x + -3.125 = 2.741464025 Simplifying x + -3.125 = 2.741464025 Reorder the terms: -3.125 + x = 2.741464025 Solving -3.125 + x = 2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 2.741464025 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 2.741464025 + 3.125 x = 2.741464025 + 3.125 Combine like terms: 2.741464025 + 3.125 = 5.866464025 x = 5.866464025 Simplifying x = 5.866464025

Subproblem 2

x + -3.125 = -2.741464025 Simplifying x + -3.125 = -2.741464025 Reorder the terms: -3.125 + x = -2.741464025 Solving -3.125 + x = -2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -2.741464025 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -2.741464025 + 3.125 x = -2.741464025 + 3.125 Combine like terms: -2.741464025 + 3.125 = 0.383535975 x = 0.383535975 Simplifying x = 0.383535975

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.866464025, 0.383535975}

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