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Simplifying 12 + 10x + 0.5x2 = 905 Solving 12 + 10x + 0.5x2 = 905 Solving for variable 'x'. Reorder the terms: 12 + -905 + 10x + 0.5x2 = 905 + -905 Combine like terms: 12 + -905 = -893 -893 + 10x + 0.5x2 = 905 + -905 Combine like terms: 905 + -905 = 0 -893 + 10x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -1786 + 20x + x2 = 0 Move the constant term to the right: Add '1786' to each side of the equation. -1786 + 20x + 1786 + x2 = 0 + 1786 Reorder the terms: -1786 + 1786 + 20x + x2 = 0 + 1786 Combine like terms: -1786 + 1786 = 0 0 + 20x + x2 = 0 + 1786 20x + x2 = 0 + 1786 Combine like terms: 0 + 1786 = 1786 20x + x2 = 1786 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 1786 + 100 Reorder the terms: 100 + 20x + x2 = 1786 + 100 Combine like terms: 1786 + 100 = 1886 100 + 20x + x2 = 1886 Factor a perfect square on the left side: (x + 10)(x + 10) = 1886 Calculate the square root of the right side: 43.428101501 Break this problem into two subproblems by setting (x + 10) equal to 43.428101501 and -43.428101501.Subproblem 1
x + 10 = 43.428101501 Simplifying x + 10 = 43.428101501 Reorder the terms: 10 + x = 43.428101501 Solving 10 + x = 43.428101501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 43.428101501 + -10 Combine like terms: 10 + -10 = 0 0 + x = 43.428101501 + -10 x = 43.428101501 + -10 Combine like terms: 43.428101501 + -10 = 33.428101501 x = 33.428101501 Simplifying x = 33.428101501Subproblem 2
x + 10 = -43.428101501 Simplifying x + 10 = -43.428101501 Reorder the terms: 10 + x = -43.428101501 Solving 10 + x = -43.428101501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -43.428101501 + -10 Combine like terms: 10 + -10 = 0 0 + x = -43.428101501 + -10 x = -43.428101501 + -10 Combine like terms: -43.428101501 + -10 = -53.428101501 x = -53.428101501 Simplifying x = -53.428101501Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.428101501, -53.428101501}
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