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Simplifying 4800 + -280x + 4x2 = 9 Solving 4800 + -280x + 4x2 = 9 Solving for variable 'x'. Reorder the terms: 4800 + -9 + -280x + 4x2 = 9 + -9 Combine like terms: 4800 + -9 = 4791 4791 + -280x + 4x2 = 9 + -9 Combine like terms: 9 + -9 = 0 4791 + -280x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1197.75 + -70x + x2 = 0 Move the constant term to the right: Add '-1197.75' to each side of the equation. 1197.75 + -70x + -1197.75 + x2 = 0 + -1197.75 Reorder the terms: 1197.75 + -1197.75 + -70x + x2 = 0 + -1197.75 Combine like terms: 1197.75 + -1197.75 = 0.00 0.00 + -70x + x2 = 0 + -1197.75 -70x + x2 = 0 + -1197.75 Combine like terms: 0 + -1197.75 = -1197.75 -70x + x2 = -1197.75 The x term is -70x. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70x + 1225 + x2 = -1197.75 + 1225 Reorder the terms: 1225 + -70x + x2 = -1197.75 + 1225 Combine like terms: -1197.75 + 1225 = 27.25 1225 + -70x + x2 = 27.25 Factor a perfect square on the left side: (x + -35)(x + -35) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + -35) equal to 5.220153254 and -5.220153254.Subproblem 1
x + -35 = 5.220153254 Simplifying x + -35 = 5.220153254 Reorder the terms: -35 + x = 5.220153254 Solving -35 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = 5.220153254 + 35 Combine like terms: -35 + 35 = 0 0 + x = 5.220153254 + 35 x = 5.220153254 + 35 Combine like terms: 5.220153254 + 35 = 40.220153254 x = 40.220153254 Simplifying x = 40.220153254Subproblem 2
x + -35 = -5.220153254 Simplifying x + -35 = -5.220153254 Reorder the terms: -35 + x = -5.220153254 Solving -35 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = -5.220153254 + 35 Combine like terms: -35 + 35 = 0 0 + x = -5.220153254 + 35 x = -5.220153254 + 35 Combine like terms: -5.220153254 + 35 = 29.779846746 x = 29.779846746 Simplifying x = 29.779846746Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.220153254, 29.779846746}
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