15x^2+40x-5=0

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Solution for 15x^2+40x-5=0 equation:


Simplifying
15x2 + 40x + -5 = 0

Reorder the terms:
-5 + 40x + 15x2 = 0

Solving
-5 + 40x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 8x + 3x2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-1 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying -1 + 8x + 3x2 = 0 Solving -1 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 2.666666667x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 2.666666667x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 2.666666667x + x2 = 0 + 0.3333333333 2.666666667x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 2.666666667x + x2 = 0.3333333333 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 0.3333333333 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 0.3333333333 + 1.777777780 Combine like terms: 0.3333333333 + 1.777777780 = 2.1111111133 1.777777780 + 2.666666667x + x2 = 2.1111111133 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 2.1111111133 Calculate the square root of the right side: 1.452966315 Break this problem into two subproblems by setting (x + 1.333333334) equal to 1.452966315 and -1.452966315.

Subproblem 1

x + 1.333333334 = 1.452966315 Simplifying x + 1.333333334 = 1.452966315 Reorder the terms: 1.333333334 + x = 1.452966315 Solving 1.333333334 + x = 1.452966315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 1.452966315 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.452966315 + -1.333333334 x = 1.452966315 + -1.333333334 Combine like terms: 1.452966315 + -1.333333334 = 0.119632981 x = 0.119632981 Simplifying x = 0.119632981

Subproblem 2

x + 1.333333334 = -1.452966315 Simplifying x + 1.333333334 = -1.452966315 Reorder the terms: 1.333333334 + x = -1.452966315 Solving 1.333333334 + x = -1.452966315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -1.452966315 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.452966315 + -1.333333334 x = -1.452966315 + -1.333333334 Combine like terms: -1.452966315 + -1.333333334 = -2.786299649 x = -2.786299649 Simplifying x = -2.786299649

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.119632981, -2.786299649}

Solution

x = {0.119632981, -2.786299649}

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