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Simplifying x2 + 12x + 24.6 = 0 Reorder the terms: 24.6 + 12x + x2 = 0 Solving 24.6 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-24.6' to each side of the equation. 24.6 + 12x + -24.6 + x2 = 0 + -24.6 Reorder the terms: 24.6 + -24.6 + 12x + x2 = 0 + -24.6 Combine like terms: 24.6 + -24.6 = 0.0 0.0 + 12x + x2 = 0 + -24.6 12x + x2 = 0 + -24.6 Combine like terms: 0 + -24.6 = -24.6 12x + x2 = -24.6 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 = -24.6 + 36 Reorder the terms: 36 + 12x + x2 = -24.6 + 36 Combine like terms: -24.6 + 36 = 11.4 36 + 12x + x2 = 11.4 Factor a perfect square on the left side: (x + 6)(x + 6) = 11.4 Calculate the square root of the right side: 3.376388603 Break this problem into two subproblems by setting (x + 6) equal to 3.376388603 and -3.376388603.Subproblem 1
x + 6 = 3.376388603 Simplifying x + 6 = 3.376388603 Reorder the terms: 6 + x = 3.376388603 Solving 6 + x = 3.376388603 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 = 3.376388603 + -6 Combine like terms: 6 + -6 = 0 0 + x = 3.376388603 + -6 x = 3.376388603 + -6 Combine like terms: 3.376388603 + -6 = -2.623611397 x = -2.623611397 Simplifying x = -2.623611397Subproblem 2
x + 6 = -3.376388603 Simplifying x + 6 = -3.376388603 Reorder the terms: 6 + x = -3.376388603 Solving 6 + x = -3.376388603 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 = -3.376388603 + -6 Combine like terms: 6 + -6 = 0 0 + x = -3.376388603 + -6 x = -3.376388603 + -6 Combine like terms: -3.376388603 + -6 = -9.376388603 x = -9.376388603 Simplifying x = -9.376388603Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.623611397, -9.376388603}
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