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Simplifying x * x + 4.53458x + -3 = 43 Multiply x * x x2 + 4.53458x + -3 = 43 Reorder the terms: -3 + 4.53458x + x2 = 43 Solving -3 + 4.53458x + x2 = 43 Solving for variable 'x'. Reorder the terms: -3 + -43 + 4.53458x + x2 = 43 + -43 Combine like terms: -3 + -43 = -46 -46 + 4.53458x + x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -46 + 4.53458x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 4.53458x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + 4.53458x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 4.53458x + x2 = 0 + 46 4.53458x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 4.53458x + x2 = 46 The x term is 4.53458x. Take half its coefficient (2.26729). Square it (5.140603944) and add it to both sides. Add '5.140603944' to each side of the equation. 4.53458x + 5.140603944 + x2 = 46 + 5.140603944 Reorder the terms: 5.140603944 + 4.53458x + x2 = 46 + 5.140603944 Combine like terms: 46 + 5.140603944 = 51.140603944 5.140603944 + 4.53458x + x2 = 51.140603944 Factor a perfect square on the left side: (x + 2.26729)(x + 2.26729) = 51.140603944 Calculate the square root of the right side: 7.151265898 Break this problem into two subproblems by setting (x + 2.26729) equal to 7.151265898 and -7.151265898.Subproblem 1
x + 2.26729 = 7.151265898 Simplifying x + 2.26729 = 7.151265898 Reorder the terms: 2.26729 + x = 7.151265898 Solving 2.26729 + x = 7.151265898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.26729' to each side of the equation. 2.26729 + -2.26729 + x = 7.151265898 + -2.26729 Combine like terms: 2.26729 + -2.26729 = 0.00000 0.00000 + x = 7.151265898 + -2.26729 x = 7.151265898 + -2.26729 Combine like terms: 7.151265898 + -2.26729 = 4.883975898 x = 4.883975898 Simplifying x = 4.883975898Subproblem 2
x + 2.26729 = -7.151265898 Simplifying x + 2.26729 = -7.151265898 Reorder the terms: 2.26729 + x = -7.151265898 Solving 2.26729 + x = -7.151265898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.26729' to each side of the equation. 2.26729 + -2.26729 + x = -7.151265898 + -2.26729 Combine like terms: 2.26729 + -2.26729 = 0.00000 0.00000 + x = -7.151265898 + -2.26729 x = -7.151265898 + -2.26729 Combine like terms: -7.151265898 + -2.26729 = -9.418555898 x = -9.418555898 Simplifying x = -9.418555898Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.883975898, -9.418555898}
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