15x^2-10x-30=0

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Solution for 15x^2-10x-30=0 equation:


Simplifying
15x2 + -10x + -30 = 0

Reorder the terms:
-30 + -10x + 15x2 = 0

Solving
-30 + -10x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + -2x + 3x2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-6 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying -6 + -2x + 3x2 = 0 Solving -6 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.6666666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.6666666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.6666666667x + x2 = 0 + 2 -0.6666666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.6666666667x + x2 = 2 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 = 2 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 2 + 0.1111111112 Combine like terms: 2 + 0.1111111112 = 2.1111111112 0.1111111112 + -0.6666666667x + x2 = 2.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 2.1111111112 Calculate the square root of the right side: 1.452966315 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 1.452966315 and -1.452966315.

Subproblem 1

x + -0.3333333334 = 1.452966315 Simplifying x + -0.3333333334 = 1.452966315 Reorder the terms: -0.3333333334 + x = 1.452966315 Solving -0.3333333334 + x = 1.452966315 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 = 1.452966315 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 1.452966315 + 0.3333333334 x = 1.452966315 + 0.3333333334 Combine like terms: 1.452966315 + 0.3333333334 = 1.7862996484 x = 1.7862996484 Simplifying x = 1.7862996484

Subproblem 2

x + -0.3333333334 = -1.452966315 Simplifying x + -0.3333333334 = -1.452966315 Reorder the terms: -0.3333333334 + x = -1.452966315 Solving -0.3333333334 + x = -1.452966315 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 = -1.452966315 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -1.452966315 + 0.3333333334 x = -1.452966315 + 0.3333333334 Combine like terms: -1.452966315 + 0.3333333334 = -1.1196329816 x = -1.1196329816 Simplifying x = -1.1196329816

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7862996484, -1.1196329816}

Solution

x = {1.7862996484, -1.1196329816}

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