4x^2-25x+35=0

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Solution for 4x^2-25x+35=0 equation:


Simplifying
4x2 + -25x + 35 = 0

Reorder the terms:
35 + -25x + 4x2 = 0

Solving
35 + -25x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
8.75 + -6.25x + x2 = 0

Move the constant term to the right:

Add '-8.75' to each side of the equation.
8.75 + -6.25x + -8.75 + x2 = 0 + -8.75

Reorder the terms:
8.75 + -8.75 + -6.25x + x2 = 0 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + -6.25x + x2 = 0 + -8.75
-6.25x + x2 = 0 + -8.75

Combine like terms: 0 + -8.75 = -8.75
-6.25x + x2 = -8.75

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 = -8.75 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = -8.75 + 9.765625

Combine like terms: -8.75 + 9.765625 = 1.015625
9.765625 + -6.25x + x2 = 1.015625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(x + -3.125) equal to 1.007782219 and -1.007782219.

Subproblem 1

x + -3.125 = 1.007782219 Simplifying x + -3.125 = 1.007782219 Reorder the terms: -3.125 + x = 1.007782219 Solving -3.125 + x = 1.007782219 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 = 1.007782219 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 1.007782219 + 3.125 x = 1.007782219 + 3.125 Combine like terms: 1.007782219 + 3.125 = 4.132782219 x = 4.132782219 Simplifying x = 4.132782219

Subproblem 2

x + -3.125 = -1.007782219 Simplifying x + -3.125 = -1.007782219 Reorder the terms: -3.125 + x = -1.007782219 Solving -3.125 + x = -1.007782219 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 = -1.007782219 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -1.007782219 + 3.125 x = -1.007782219 + 3.125 Combine like terms: -1.007782219 + 3.125 = 2.117217781 x = 2.117217781 Simplifying x = 2.117217781

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.132782219, 2.117217781}

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