30x^2-20x-10=8

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Solution for 30x^2-20x-10=8 equation:


Simplifying
30x2 + -20x + -10 = 8

Reorder the terms:
-10 + -20x + 30x2 = 8

Solving
-10 + -20x + 30x2 = 8

Solving for variable 'x'.

Reorder the terms:
-10 + -8 + -20x + 30x2 = 8 + -8

Combine like terms: -10 + -8 = -18
-18 + -20x + 30x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-18 + -20x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -10x + 15x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-9 + -10x + 15x2)' equal to zero and attempt to solve: Simplifying -9 + -10x + 15x2 = 0 Solving -9 + -10x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.6 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.6666666667x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.6666666667x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.6666666667x + x2 = 0 + 0.6 -0.6666666667x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.6666666667x + x2 = 0.6 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 = 0.6 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 0.6 + 0.1111111112 Combine like terms: 0.6 + 0.1111111112 = 0.7111111112 0.1111111112 + -0.6666666667x + x2 = 0.7111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 0.7111111112 Calculate the square root of the right side: 0.843274043 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 0.843274043 and -0.843274043.

Subproblem 1

x + -0.3333333334 = 0.843274043 Simplifying x + -0.3333333334 = 0.843274043 Reorder the terms: -0.3333333334 + x = 0.843274043 Solving -0.3333333334 + x = 0.843274043 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 = 0.843274043 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 0.843274043 + 0.3333333334 x = 0.843274043 + 0.3333333334 Combine like terms: 0.843274043 + 0.3333333334 = 1.1766073764 x = 1.1766073764 Simplifying x = 1.1766073764

Subproblem 2

x + -0.3333333334 = -0.843274043 Simplifying x + -0.3333333334 = -0.843274043 Reorder the terms: -0.3333333334 + x = -0.843274043 Solving -0.3333333334 + x = -0.843274043 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 = -0.843274043 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -0.843274043 + 0.3333333334 x = -0.843274043 + 0.3333333334 Combine like terms: -0.843274043 + 0.3333333334 = -0.5099407096 x = -0.5099407096 Simplifying x = -0.5099407096

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1766073764, -0.5099407096}

Solution

x = {1.1766073764, -0.5099407096}

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