30x^2-2x-10=0

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Solution for 30x^2-2x-10=0 equation:


Simplifying
30x2 + -2x + -10 = 0

Reorder the terms:
-10 + -2x + 30x2 = 0

Solving
-10 + -2x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -1x + 15x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -1x + 15x2)' equal to zero and attempt to solve: Simplifying -5 + -1x + 15x2 = 0 Solving -5 + -1x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.3333333333 + -0.06666666667x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.06666666667x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.06666666667x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.06666666667x + x2 = 0 + 0.3333333333 -0.06666666667x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.06666666667x + x2 = 0.3333333333 The x term is -0.06666666667x. Take half its coefficient (-0.03333333334). Square it (0.001111111112) and add it to both sides. Add '0.001111111112' to each side of the equation. -0.06666666667x + 0.001111111112 + x2 = 0.3333333333 + 0.001111111112 Reorder the terms: 0.001111111112 + -0.06666666667x + x2 = 0.3333333333 + 0.001111111112 Combine like terms: 0.3333333333 + 0.001111111112 = 0.334444444412 0.001111111112 + -0.06666666667x + x2 = 0.334444444412 Factor a perfect square on the left side: (x + -0.03333333334)(x + -0.03333333334) = 0.334444444412 Calculate the square root of the right side: 0.578311719 Break this problem into two subproblems by setting (x + -0.03333333334) equal to 0.578311719 and -0.578311719.

Subproblem 1

x + -0.03333333334 = 0.578311719 Simplifying x + -0.03333333334 = 0.578311719 Reorder the terms: -0.03333333334 + x = 0.578311719 Solving -0.03333333334 + x = 0.578311719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03333333334' to each side of the equation. -0.03333333334 + 0.03333333334 + x = 0.578311719 + 0.03333333334 Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000 0.00000000000 + x = 0.578311719 + 0.03333333334 x = 0.578311719 + 0.03333333334 Combine like terms: 0.578311719 + 0.03333333334 = 0.61164505234 x = 0.61164505234 Simplifying x = 0.61164505234

Subproblem 2

x + -0.03333333334 = -0.578311719 Simplifying x + -0.03333333334 = -0.578311719 Reorder the terms: -0.03333333334 + x = -0.578311719 Solving -0.03333333334 + x = -0.578311719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03333333334' to each side of the equation. -0.03333333334 + 0.03333333334 + x = -0.578311719 + 0.03333333334 Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000 0.00000000000 + x = -0.578311719 + 0.03333333334 x = -0.578311719 + 0.03333333334 Combine like terms: -0.578311719 + 0.03333333334 = -0.54497838566 x = -0.54497838566 Simplifying x = -0.54497838566

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.61164505234, -0.54497838566}

Solution

x = {0.61164505234, -0.54497838566}

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