x^2+5x^2-4x-20=0

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Solution for x^2+5x^2-4x-20=0 equation:


Simplifying
x2 + 5x2 + -4x + -20 = 0

Reorder the terms:
-20 + -4x + x2 + 5x2 = 0

Combine like terms: x2 + 5x2 = 6x2
-20 + -4x + 6x2 = 0

Solving
-20 + -4x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -2x + 3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-10 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying -10 + -2x + 3x2 = 0 Solving -10 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -0.6666666667x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -0.6666666667x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + 3.333333333 -0.6666666667x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -0.6666666667x + x2 = 3.333333333 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 = 3.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 3.333333333 + 0.1111111112 Combine like terms: 3.333333333 + 0.1111111112 = 3.4444444442 0.1111111112 + -0.6666666667x + x2 = 3.4444444442 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 3.4444444442 Calculate the square root of the right side: 1.855921454 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 1.855921454 and -1.855921454.

Subproblem 1

x + -0.3333333334 = 1.855921454 Simplifying x + -0.3333333334 = 1.855921454 Reorder the terms: -0.3333333334 + x = 1.855921454 Solving -0.3333333334 + x = 1.855921454 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 = 1.855921454 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 1.855921454 + 0.3333333334 x = 1.855921454 + 0.3333333334 Combine like terms: 1.855921454 + 0.3333333334 = 2.1892547874 x = 2.1892547874 Simplifying x = 2.1892547874

Subproblem 2

x + -0.3333333334 = -1.855921454 Simplifying x + -0.3333333334 = -1.855921454 Reorder the terms: -0.3333333334 + x = -1.855921454 Solving -0.3333333334 + x = -1.855921454 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 = -1.855921454 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -1.855921454 + 0.3333333334 x = -1.855921454 + 0.3333333334 Combine like terms: -1.855921454 + 0.3333333334 = -1.5225881206 x = -1.5225881206 Simplifying x = -1.5225881206

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.1892547874, -1.5225881206}

Solution

x = {2.1892547874, -1.5225881206}

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