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Simplifying 12x2 + x + -14 = 0 Reorder the terms: -14 + x + 12x2 = 0 Solving -14 + x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.166666667 + 0.08333333333x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + 0.08333333333x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + 0.08333333333x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + 0.08333333333x + x2 = 0 + 1.166666667 0.08333333333x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 0.08333333333x + x2 = 1.166666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.08333333333x + 0.25 + x2 = 1.166666667 + 0.25 Reorder the terms: 0.25 + 0.08333333333x + x2 = 1.166666667 + 0.25 Combine like terms: 1.166666667 + 0.25 = 1.416666667 0.25 + 0.08333333333x + x2 = 1.416666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.416666667 Calculate the square root of the right side: 1.190238072 Break this problem into two subproblems by setting (x + 0.5) equal to 1.190238072 and -1.190238072.Subproblem 1
x + 0.5 = 1.190238072 Simplifying x + 0.5 = 1.190238072 Reorder the terms: 0.5 + x = 1.190238072 Solving 0.5 + x = 1.190238072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.190238072 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.190238072 + -0.5 x = 1.190238072 + -0.5 Combine like terms: 1.190238072 + -0.5 = 0.690238072 x = 0.690238072 Simplifying x = 0.690238072Subproblem 2
x + 0.5 = -1.190238072 Simplifying x + 0.5 = -1.190238072 Reorder the terms: 0.5 + x = -1.190238072 Solving 0.5 + x = -1.190238072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.190238072 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.190238072 + -0.5 x = -1.190238072 + -0.5 Combine like terms: -1.190238072 + -0.5 = -1.690238072 x = -1.690238072 Simplifying x = -1.690238072Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.690238072, -1.690238072}
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