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Simplifying -0.25x2 + 110x + -9600 = 0 Reorder the terms: -9600 + 110x + -0.25x2 = 0 Solving -9600 + 110x + -0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. 38400 + -440x + x2 = 0 Move the constant term to the right: Add '-38400' to each side of the equation. 38400 + -440x + -38400 + x2 = 0 + -38400 Reorder the terms: 38400 + -38400 + -440x + x2 = 0 + -38400 Combine like terms: 38400 + -38400 = 0 0 + -440x + x2 = 0 + -38400 -440x + x2 = 0 + -38400 Combine like terms: 0 + -38400 = -38400 -440x + x2 = -38400 The x term is -440x. Take half its coefficient (-220). Square it (48400) and add it to both sides. Add '48400' to each side of the equation. -440x + 48400 + x2 = -38400 + 48400 Reorder the terms: 48400 + -440x + x2 = -38400 + 48400 Combine like terms: -38400 + 48400 = 10000 48400 + -440x + x2 = 10000 Factor a perfect square on the left side: (x + -220)(x + -220) = 10000 Calculate the square root of the right side: 100 Break this problem into two subproblems by setting (x + -220) equal to 100 and -100.Subproblem 1
x + -220 = 100 Simplifying x + -220 = 100 Reorder the terms: -220 + x = 100 Solving -220 + x = 100 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '220' to each side of the equation. -220 + 220 + x = 100 + 220 Combine like terms: -220 + 220 = 0 0 + x = 100 + 220 x = 100 + 220 Combine like terms: 100 + 220 = 320 x = 320 Simplifying x = 320Subproblem 2
x + -220 = -100 Simplifying x + -220 = -100 Reorder the terms: -220 + x = -100 Solving -220 + x = -100 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '220' to each side of the equation. -220 + 220 + x = -100 + 220 Combine like terms: -220 + 220 = 0 0 + x = -100 + 220 x = -100 + 220 Combine like terms: -100 + 220 = 120 x = 120 Simplifying x = 120Solution
The solution to the problem is based on the solutions from the subproblems. x = {320, 120}
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