25x^2-70x=49

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Solution for 25x^2-70x=49 equation:


Simplifying
25x2 + -70x = 49

Reorder the terms:
-70x + 25x2 = 49

Solving
-70x + 25x2 = 49

Solving for variable 'x'.

Reorder the terms:
-49 + -70x + 25x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + -70x + 25x2 = 0

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

Divide each side by '25'.
-1.96 + -2.8x + x2 = 0

Move the constant term to the right:

Add '1.96' to each side of the equation.
-1.96 + -2.8x + 1.96 + x2 = 0 + 1.96

Reorder the terms:
-1.96 + 1.96 + -2.8x + x2 = 0 + 1.96

Combine like terms: -1.96 + 1.96 = 0.00
0.00 + -2.8x + x2 = 0 + 1.96
-2.8x + x2 = 0 + 1.96

Combine like terms: 0 + 1.96 = 1.96
-2.8x + x2 = 1.96

The x term is -2.8x.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8x + 1.96 + x2 = 1.96 + 1.96

Reorder the terms:
1.96 + -2.8x + x2 = 1.96 + 1.96

Combine like terms: 1.96 + 1.96 = 3.92
1.96 + -2.8x + x2 = 3.92

Factor a perfect square on the left side:
(x + -1.4)(x + -1.4) = 3.92

Calculate the square root of the right side: 1.979898987

Break this problem into two subproblems by setting 
(x + -1.4) equal to 1.979898987 and -1.979898987.

Subproblem 1

x + -1.4 = 1.979898987 Simplifying x + -1.4 = 1.979898987 Reorder the terms: -1.4 + x = 1.979898987 Solving -1.4 + x = 1.979898987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 1.979898987 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 1.979898987 + 1.4 x = 1.979898987 + 1.4 Combine like terms: 1.979898987 + 1.4 = 3.379898987 x = 3.379898987 Simplifying x = 3.379898987

Subproblem 2

x + -1.4 = -1.979898987 Simplifying x + -1.4 = -1.979898987 Reorder the terms: -1.4 + x = -1.979898987 Solving -1.4 + x = -1.979898987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -1.979898987 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -1.979898987 + 1.4 x = -1.979898987 + 1.4 Combine like terms: -1.979898987 + 1.4 = -0.579898987 x = -0.579898987 Simplifying x = -0.579898987

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.379898987, -0.579898987}

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