35x^2-65x+25=0

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Solution for 35x^2-65x+25=0 equation:


Simplifying
35x2 + -65x + 25 = 0

Reorder the terms:
25 + -65x + 35x2 = 0

Solving
25 + -65x + 35x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + -13x + 7x2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(5 + -13x + 7x2)' equal to zero and attempt to solve: Simplifying 5 + -13x + 7x2 = 0 Solving 5 + -13x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.7142857143 + -1.857142857x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -1.857142857x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -1.857142857x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -1.857142857x + x2 = 0 + -0.7142857143 -1.857142857x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -1.857142857x + x2 = -0.7142857143 The x term is -1.857142857x. Take half its coefficient (-0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. -1.857142857x + 0.8622448978 + x2 = -0.7142857143 + 0.8622448978 Reorder the terms: 0.8622448978 + -1.857142857x + x2 = -0.7142857143 + 0.8622448978 Combine like terms: -0.7142857143 + 0.8622448978 = 0.1479591835 0.8622448978 + -1.857142857x + x2 = 0.1479591835 Factor a perfect square on the left side: (x + -0.9285714285)(x + -0.9285714285) = 0.1479591835 Calculate the square root of the right side: 0.384654629 Break this problem into two subproblems by setting (x + -0.9285714285) equal to 0.384654629 and -0.384654629.

Subproblem 1

x + -0.9285714285 = 0.384654629 Simplifying x + -0.9285714285 = 0.384654629 Reorder the terms: -0.9285714285 + x = 0.384654629 Solving -0.9285714285 + x = 0.384654629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + x = 0.384654629 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = 0.384654629 + 0.9285714285 x = 0.384654629 + 0.9285714285 Combine like terms: 0.384654629 + 0.9285714285 = 1.3132260575 x = 1.3132260575 Simplifying x = 1.3132260575

Subproblem 2

x + -0.9285714285 = -0.384654629 Simplifying x + -0.9285714285 = -0.384654629 Reorder the terms: -0.9285714285 + x = -0.384654629 Solving -0.9285714285 + x = -0.384654629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + x = -0.384654629 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = -0.384654629 + 0.9285714285 x = -0.384654629 + 0.9285714285 Combine like terms: -0.384654629 + 0.9285714285 = 0.5439167995 x = 0.5439167995 Simplifying x = 0.5439167995

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.3132260575, 0.5439167995}

Solution

x = {1.3132260575, 0.5439167995}

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