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Simplifying 0.012x2 + -0.543x + -14.278 = 0 Reorder the terms: -14.278 + -0.543x + 0.012x2 = 0 Solving -14.278 + -0.543x + 0.012x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.012 the coefficient of the squared term: Divide each side by '0.012'. -1189.833333 + -45.25x + x2 = 0 Move the constant term to the right: Add '1189.833333' to each side of the equation. -1189.833333 + -45.25x + 1189.833333 + x2 = 0 + 1189.833333 Reorder the terms: -1189.833333 + 1189.833333 + -45.25x + x2 = 0 + 1189.833333 Combine like terms: -1189.833333 + 1189.833333 = 0.000000 0.000000 + -45.25x + x2 = 0 + 1189.833333 -45.25x + x2 = 0 + 1189.833333 Combine like terms: 0 + 1189.833333 = 1189.833333 -45.25x + x2 = 1189.833333 The x term is -45.25x. Take half its coefficient (-22.625). Square it (511.890625) and add it to both sides. Add '511.890625' to each side of the equation. -45.25x + 511.890625 + x2 = 1189.833333 + 511.890625 Reorder the terms: 511.890625 + -45.25x + x2 = 1189.833333 + 511.890625 Combine like terms: 1189.833333 + 511.890625 = 1701.723958 511.890625 + -45.25x + x2 = 1701.723958 Factor a perfect square on the left side: (x + -22.625)(x + -22.625) = 1701.723958 Calculate the square root of the right side: 41.25195702 Break this problem into two subproblems by setting (x + -22.625) equal to 41.25195702 and -41.25195702.Subproblem 1
x + -22.625 = 41.25195702 Simplifying x + -22.625 = 41.25195702 Reorder the terms: -22.625 + x = 41.25195702 Solving -22.625 + x = 41.25195702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.625' to each side of the equation. -22.625 + 22.625 + x = 41.25195702 + 22.625 Combine like terms: -22.625 + 22.625 = 0.000 0.000 + x = 41.25195702 + 22.625 x = 41.25195702 + 22.625 Combine like terms: 41.25195702 + 22.625 = 63.87695702 x = 63.87695702 Simplifying x = 63.87695702Subproblem 2
x + -22.625 = -41.25195702 Simplifying x + -22.625 = -41.25195702 Reorder the terms: -22.625 + x = -41.25195702 Solving -22.625 + x = -41.25195702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.625' to each side of the equation. -22.625 + 22.625 + x = -41.25195702 + 22.625 Combine like terms: -22.625 + 22.625 = 0.000 0.000 + x = -41.25195702 + 22.625 x = -41.25195702 + 22.625 Combine like terms: -41.25195702 + 22.625 = -18.62695702 x = -18.62695702 Simplifying x = -18.62695702Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.87695702, -18.62695702}
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