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Simplifying 24x2 = 2 + -14x Solving 24x2 = 2 + -14x Solving for variable 'x'. Reorder the terms: -2 + 14x + 24x2 = 2 + -14x + -2 + 14x Reorder the terms: -2 + 14x + 24x2 = 2 + -2 + -14x + 14x Combine like terms: 2 + -2 = 0 -2 + 14x + 24x2 = 0 + -14x + 14x -2 + 14x + 24x2 = -14x + 14x Combine like terms: -14x + 14x = 0 -2 + 14x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 7x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 7x + 12x2)' equal to zero and attempt to solve: Simplifying -1 + 7x + 12x2 = 0 Solving -1 + 7x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.08333333333 + 0.5833333333x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.5833333333x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.5833333333x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.5833333333x + x2 = 0 + 0.08333333333 0.5833333333x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.5833333333x + x2 = 0.08333333333 The x term is 0.5833333333x. Take half its coefficient (0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. 0.5833333333x + 0.08506944446 + x2 = 0.08333333333 + 0.08506944446 Reorder the terms: 0.08506944446 + 0.5833333333x + x2 = 0.08333333333 + 0.08506944446 Combine like terms: 0.08333333333 + 0.08506944446 = 0.16840277779 0.08506944446 + 0.5833333333x + x2 = 0.16840277779 Factor a perfect square on the left side: (x + 0.2916666667)(x + 0.2916666667) = 0.16840277779 Calculate the square root of the right side: 0.410369075 Break this problem into two subproblems by setting (x + 0.2916666667) equal to 0.410369075 and -0.410369075.Subproblem 1
x + 0.2916666667 = 0.410369075 Simplifying x + 0.2916666667 = 0.410369075 Reorder the terms: 0.2916666667 + x = 0.410369075 Solving 0.2916666667 + x = 0.410369075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2916666667' to each side of the equation. 0.2916666667 + -0.2916666667 + x = 0.410369075 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + x = 0.410369075 + -0.2916666667 x = 0.410369075 + -0.2916666667 Combine like terms: 0.410369075 + -0.2916666667 = 0.1187024083 x = 0.1187024083 Simplifying x = 0.1187024083Subproblem 2
x + 0.2916666667 = -0.410369075 Simplifying x + 0.2916666667 = -0.410369075 Reorder the terms: 0.2916666667 + x = -0.410369075 Solving 0.2916666667 + x = -0.410369075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2916666667' to each side of the equation. 0.2916666667 + -0.2916666667 + x = -0.410369075 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + x = -0.410369075 + -0.2916666667 x = -0.410369075 + -0.2916666667 Combine like terms: -0.410369075 + -0.2916666667 = -0.7020357417 x = -0.7020357417 Simplifying x = -0.7020357417Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1187024083, -0.7020357417}Solution
x = {0.1187024083, -0.7020357417}
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