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Simplifying 7x2 + -202.3x + 1453.9 = 0 Reorder the terms: 1453.9 + -202.3x + 7x2 = 0 Solving 1453.9 + -202.3x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 207.7 + -28.9x + x2 = 0 Move the constant term to the right: Add '-207.7' to each side of the equation. 207.7 + -28.9x + -207.7 + x2 = 0 + -207.7 Reorder the terms: 207.7 + -207.7 + -28.9x + x2 = 0 + -207.7 Combine like terms: 207.7 + -207.7 = 0.0 0.0 + -28.9x + x2 = 0 + -207.7 -28.9x + x2 = 0 + -207.7 Combine like terms: 0 + -207.7 = -207.7 -28.9x + x2 = -207.7 The x term is -28.9x. Take half its coefficient (-14.45). Square it (208.8025) and add it to both sides. Add '208.8025' to each side of the equation. -28.9x + 208.8025 + x2 = -207.7 + 208.8025 Reorder the terms: 208.8025 + -28.9x + x2 = -207.7 + 208.8025 Combine like terms: -207.7 + 208.8025 = 1.1025 208.8025 + -28.9x + x2 = 1.1025 Factor a perfect square on the left side: (x + -14.45)(x + -14.45) = 1.1025 Calculate the square root of the right side: 1.05 Break this problem into two subproblems by setting (x + -14.45) equal to 1.05 and -1.05.Subproblem 1
x + -14.45 = 1.05 Simplifying x + -14.45 = 1.05 Reorder the terms: -14.45 + x = 1.05 Solving -14.45 + x = 1.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.45' to each side of the equation. -14.45 + 14.45 + x = 1.05 + 14.45 Combine like terms: -14.45 + 14.45 = 0.00 0.00 + x = 1.05 + 14.45 x = 1.05 + 14.45 Combine like terms: 1.05 + 14.45 = 15.5 x = 15.5 Simplifying x = 15.5Subproblem 2
x + -14.45 = -1.05 Simplifying x + -14.45 = -1.05 Reorder the terms: -14.45 + x = -1.05 Solving -14.45 + x = -1.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.45' to each side of the equation. -14.45 + 14.45 + x = -1.05 + 14.45 Combine like terms: -14.45 + 14.45 = 0.00 0.00 + x = -1.05 + 14.45 x = -1.05 + 14.45 Combine like terms: -1.05 + 14.45 = 13.4 x = 13.4 Simplifying x = 13.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.5, 13.4}
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