25x^2-30x+7=0

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Solution for 25x^2-30x+7=0 equation:


Simplifying
25x2 + -30x + 7 = 0

Reorder the terms:
7 + -30x + 25x2 = 0

Solving
7 + -30x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
0.28 + -1.2x + x2 = 0

Move the constant term to the right:

Add '-0.28' to each side of the equation.
0.28 + -1.2x + -0.28 + x2 = 0 + -0.28

Reorder the terms:
0.28 + -0.28 + -1.2x + x2 = 0 + -0.28

Combine like terms: 0.28 + -0.28 = 0.00
0.00 + -1.2x + x2 = 0 + -0.28
-1.2x + x2 = 0 + -0.28

Combine like terms: 0 + -0.28 = -0.28
-1.2x + x2 = -0.28

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = -0.28 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = -0.28 + 0.36

Combine like terms: -0.28 + 0.36 = 0.08
0.36 + -1.2x + x2 = 0.08

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 0.08

Calculate the square root of the right side: 0.282842712

Break this problem into two subproblems by setting 
(x + -0.6) equal to 0.282842712 and -0.282842712.

Subproblem 1

x + -0.6 = 0.282842712 Simplifying x + -0.6 = 0.282842712 Reorder the terms: -0.6 + x = 0.282842712 Solving -0.6 + x = 0.282842712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.282842712 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.282842712 + 0.6 x = 0.282842712 + 0.6 Combine like terms: 0.282842712 + 0.6 = 0.882842712 x = 0.882842712 Simplifying x = 0.882842712

Subproblem 2

x + -0.6 = -0.282842712 Simplifying x + -0.6 = -0.282842712 Reorder the terms: -0.6 + x = -0.282842712 Solving -0.6 + x = -0.282842712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.282842712 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.282842712 + 0.6 x = -0.282842712 + 0.6 Combine like terms: -0.282842712 + 0.6 = 0.317157288 x = 0.317157288 Simplifying x = 0.317157288

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.882842712, 0.317157288}

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