4x^2-35x+40=0

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Solution for 4x^2-35x+40=0 equation:


Simplifying
4x2 + -35x + 40 = 0

Reorder the terms:
40 + -35x + 4x2 = 0

Solving
40 + -35x + 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'.
10 + -8.75x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -8.75x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -8.75x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -8.75x + x2 = 0 + -10
-8.75x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-8.75x + x2 = -10

The x term is -8.75x.  Take half its coefficient (-4.375).
Square it (19.140625) and add it to both sides.

Add '19.140625' to each side of the equation.
-8.75x + 19.140625 + x2 = -10 + 19.140625

Reorder the terms:
19.140625 + -8.75x + x2 = -10 + 19.140625

Combine like terms: -10 + 19.140625 = 9.140625
19.140625 + -8.75x + x2 = 9.140625

Factor a perfect square on the left side:
(x + -4.375)(x + -4.375) = 9.140625

Calculate the square root of the right side: 3.023346656

Break this problem into two subproblems by setting 
(x + -4.375) equal to 3.023346656 and -3.023346656.

Subproblem 1

x + -4.375 = 3.023346656 Simplifying x + -4.375 = 3.023346656 Reorder the terms: -4.375 + x = 3.023346656 Solving -4.375 + x = 3.023346656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = 3.023346656 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 3.023346656 + 4.375 x = 3.023346656 + 4.375 Combine like terms: 3.023346656 + 4.375 = 7.398346656 x = 7.398346656 Simplifying x = 7.398346656

Subproblem 2

x + -4.375 = -3.023346656 Simplifying x + -4.375 = -3.023346656 Reorder the terms: -4.375 + x = -3.023346656 Solving -4.375 + x = -3.023346656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = -3.023346656 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -3.023346656 + 4.375 x = -3.023346656 + 4.375 Combine like terms: -3.023346656 + 4.375 = 1.351653344 x = 1.351653344 Simplifying x = 1.351653344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.398346656, 1.351653344}

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