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Simplifying 147x + 406 + -10x2 = 0 Reorder the terms: 406 + 147x + -10x2 = 0 Solving 406 + 147x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -40.6 + -14.7x + x2 = 0 Move the constant term to the right: Add '40.6' to each side of the equation. -40.6 + -14.7x + 40.6 + x2 = 0 + 40.6 Reorder the terms: -40.6 + 40.6 + -14.7x + x2 = 0 + 40.6 Combine like terms: -40.6 + 40.6 = 0.0 0.0 + -14.7x + x2 = 0 + 40.6 -14.7x + x2 = 0 + 40.6 Combine like terms: 0 + 40.6 = 40.6 -14.7x + x2 = 40.6 The x term is -14.7x. Take half its coefficient (-7.35). Square it (54.0225) and add it to both sides. Add '54.0225' to each side of the equation. -14.7x + 54.0225 + x2 = 40.6 + 54.0225 Reorder the terms: 54.0225 + -14.7x + x2 = 40.6 + 54.0225 Combine like terms: 40.6 + 54.0225 = 94.6225 54.0225 + -14.7x + x2 = 94.6225 Factor a perfect square on the left side: (x + -7.35)(x + -7.35) = 94.6225 Calculate the square root of the right side: 9.727409727 Break this problem into two subproblems by setting (x + -7.35) equal to 9.727409727 and -9.727409727.Subproblem 1
x + -7.35 = 9.727409727 Simplifying x + -7.35 = 9.727409727 Reorder the terms: -7.35 + x = 9.727409727 Solving -7.35 + x = 9.727409727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.35' to each side of the equation. -7.35 + 7.35 + x = 9.727409727 + 7.35 Combine like terms: -7.35 + 7.35 = 0.00 0.00 + x = 9.727409727 + 7.35 x = 9.727409727 + 7.35 Combine like terms: 9.727409727 + 7.35 = 17.077409727 x = 17.077409727 Simplifying x = 17.077409727Subproblem 2
x + -7.35 = -9.727409727 Simplifying x + -7.35 = -9.727409727 Reorder the terms: -7.35 + x = -9.727409727 Solving -7.35 + x = -9.727409727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.35' to each side of the equation. -7.35 + 7.35 + x = -9.727409727 + 7.35 Combine like terms: -7.35 + 7.35 = 0.00 0.00 + x = -9.727409727 + 7.35 x = -9.727409727 + 7.35 Combine like terms: -9.727409727 + 7.35 = -2.377409727 x = -2.377409727 Simplifying x = -2.377409727Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.077409727, -2.377409727}
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