72x^2+60x-24=0

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Solution for 72x^2+60x-24=0 equation:


Simplifying
72x2 + 60x + -24 = 0

Reorder the terms:
-24 + 60x + 72x2 = 0

Solving
-24 + 60x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-2 + 5x + 6x2) = 0

Ignore the factor 12.

Subproblem 1

Set the factor '(-2 + 5x + 6x2)' equal to zero and attempt to solve: Simplifying -2 + 5x + 6x2 = 0 Solving -2 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.3333333333 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.8333333333x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.8333333333x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.8333333333x + x2 = 0 + 0.3333333333 0.8333333333x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.8333333333x + x2 = 0.3333333333 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 0.3333333333 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 0.3333333333 + 0.1736111111 Combine like terms: 0.3333333333 + 0.1736111111 = 0.5069444444 0.1736111111 + 0.8333333333x + x2 = 0.5069444444 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 0.5069444444 Calculate the square root of the right side: 0.712000312 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 0.712000312 and -0.712000312.

Subproblem 1

x + 0.4166666667 = 0.712000312 Simplifying x + 0.4166666667 = 0.712000312 Reorder the terms: 0.4166666667 + x = 0.712000312 Solving 0.4166666667 + x = 0.712000312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 0.712000312 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 0.712000312 + -0.4166666667 x = 0.712000312 + -0.4166666667 Combine like terms: 0.712000312 + -0.4166666667 = 0.2953336453 x = 0.2953336453 Simplifying x = 0.2953336453

Subproblem 2

x + 0.4166666667 = -0.712000312 Simplifying x + 0.4166666667 = -0.712000312 Reorder the terms: 0.4166666667 + x = -0.712000312 Solving 0.4166666667 + x = -0.712000312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -0.712000312 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -0.712000312 + -0.4166666667 x = -0.712000312 + -0.4166666667 Combine like terms: -0.712000312 + -0.4166666667 = -1.1286669787 x = -1.1286669787 Simplifying x = -1.1286669787

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2953336453, -1.1286669787}

Solution

x = {0.2953336453, -1.1286669787}

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