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Simplifying 12x2 + 118x + -10 = 0 Reorder the terms: -10 + 118x + 12x2 = 0 Solving -10 + 118x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 59x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 59x + 6x2)' equal to zero and attempt to solve: Simplifying -5 + 59x + 6x2 = 0 Solving -5 + 59x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + 9.833333333x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 9.833333333x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 9.833333333x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 9.833333333x + x2 = 0 + 0.8333333333 9.833333333x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 9.833333333x + x2 = 0.8333333333 The x term is 9.833333333x. Take half its coefficient (4.916666667). Square it (24.17361111) and add it to both sides. Add '24.17361111' to each side of the equation. 9.833333333x + 24.17361111 + x2 = 0.8333333333 + 24.17361111 Reorder the terms: 24.17361111 + 9.833333333x + x2 = 0.8333333333 + 24.17361111 Combine like terms: 0.8333333333 + 24.17361111 = 25.0069444433 24.17361111 + 9.833333333x + x2 = 25.0069444433 Factor a perfect square on the left side: (x + 4.916666667)(x + 4.916666667) = 25.0069444433 Calculate the square root of the right side: 5.000694396 Break this problem into two subproblems by setting (x + 4.916666667) equal to 5.000694396 and -5.000694396.Subproblem 1
x + 4.916666667 = 5.000694396 Simplifying x + 4.916666667 = 5.000694396 Reorder the terms: 4.916666667 + x = 5.000694396 Solving 4.916666667 + x = 5.000694396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.916666667' to each side of the equation. 4.916666667 + -4.916666667 + x = 5.000694396 + -4.916666667 Combine like terms: 4.916666667 + -4.916666667 = 0.000000000 0.000000000 + x = 5.000694396 + -4.916666667 x = 5.000694396 + -4.916666667 Combine like terms: 5.000694396 + -4.916666667 = 0.084027729 x = 0.084027729 Simplifying x = 0.084027729Subproblem 2
x + 4.916666667 = -5.000694396 Simplifying x + 4.916666667 = -5.000694396 Reorder the terms: 4.916666667 + x = -5.000694396 Solving 4.916666667 + x = -5.000694396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.916666667' to each side of the equation. 4.916666667 + -4.916666667 + x = -5.000694396 + -4.916666667 Combine like terms: 4.916666667 + -4.916666667 = 0.000000000 0.000000000 + x = -5.000694396 + -4.916666667 x = -5.000694396 + -4.916666667 Combine like terms: -5.000694396 + -4.916666667 = -9.917361063 x = -9.917361063 Simplifying x = -9.917361063Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.084027729, -9.917361063}Solution
x = {0.084027729, -9.917361063}
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