6x^2-40=4x

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Solution for 6x^2-40=4x equation:


Simplifying
6x2 + -40 = 4x

Reorder the terms:
-40 + 6x2 = 4x

Solving
-40 + 6x2 = 4x

Solving for variable 'x'.

Reorder the terms:
-40 + -4x + 6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-40 + -4x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -2x + 3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-20 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying -20 + -2x + 3x2 = 0 Solving -20 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.666666667 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -0.6666666667x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -0.6666666667x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + 6.666666667 -0.6666666667x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -0.6666666667x + x2 = 6.666666667 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 6.666666667 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 6.666666667 + 0.1111111112 Combine like terms: 6.666666667 + 0.1111111112 = 6.7777777782 0.1111111112 + -0.6666666667x + x2 = 6.7777777782 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 6.7777777782 Calculate the square root of the right side: 2.603416559 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 2.603416559 and -2.603416559.

Subproblem 1

x + -0.3333333334 = 2.603416559 Simplifying x + -0.3333333334 = 2.603416559 Reorder the terms: -0.3333333334 + x = 2.603416559 Solving -0.3333333334 + x = 2.603416559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 2.603416559 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 2.603416559 + 0.3333333334 x = 2.603416559 + 0.3333333334 Combine like terms: 2.603416559 + 0.3333333334 = 2.9367498924 x = 2.9367498924 Simplifying x = 2.9367498924

Subproblem 2

x + -0.3333333334 = -2.603416559 Simplifying x + -0.3333333334 = -2.603416559 Reorder the terms: -0.3333333334 + x = -2.603416559 Solving -0.3333333334 + x = -2.603416559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -2.603416559 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -2.603416559 + 0.3333333334 x = -2.603416559 + 0.3333333334 Combine like terms: -2.603416559 + 0.3333333334 = -2.2700832256 x = -2.2700832256 Simplifying x = -2.2700832256

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.9367498924, -2.2700832256}

Solution

x = {2.9367498924, -2.2700832256}

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