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Simplifying 10x2 + 120x + -36 = 0 Reorder the terms: -36 + 120x + 10x2 = 0 Solving -36 + 120x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 60x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + 60x + 5x2)' equal to zero and attempt to solve: Simplifying -18 + 60x + 5x2 = 0 Solving -18 + 60x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + 12x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 12x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 12x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 12x + x2 = 0 + 3.6 12x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 12x + x2 = 3.6 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 3.6 + 36 Reorder the terms: 36 + 12x + x2 = 3.6 + 36 Combine like terms: 3.6 + 36 = 39.6 36 + 12x + x2 = 39.6 Factor a perfect square on the left side: (x + 6)(x + 6) = 39.6 Calculate the square root of the right side: 6.292853089 Break this problem into two subproblems by setting (x + 6) equal to 6.292853089 and -6.292853089.Subproblem 1
x + 6 = 6.292853089 Simplifying x + 6 = 6.292853089 Reorder the terms: 6 + x = 6.292853089 Solving 6 + x = 6.292853089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.292853089 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.292853089 + -6 x = 6.292853089 + -6 Combine like terms: 6.292853089 + -6 = 0.292853089 x = 0.292853089 Simplifying x = 0.292853089Subproblem 2
x + 6 = -6.292853089 Simplifying x + 6 = -6.292853089 Reorder the terms: 6 + x = -6.292853089 Solving 6 + x = -6.292853089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.292853089 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.292853089 + -6 x = -6.292853089 + -6 Combine like terms: -6.292853089 + -6 = -12.292853089 x = -12.292853089 Simplifying x = -12.292853089Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.292853089, -12.292853089}Solution
x = {0.292853089, -12.292853089}
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