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Simplifying 137x + -0.125x2 = 32930 Solving 137x + -0.125x2 = 32930 Solving for variable 'x'. Reorder the terms: -32930 + 137x + -0.125x2 = 32930 + -32930 Combine like terms: 32930 + -32930 = 0 -32930 + 137x + -0.125x2 = 0 Begin completing the square. Divide all terms by -0.125 the coefficient of the squared term: Divide each side by '-0.125'. 263440 + -1096x + x2 = 0 Move the constant term to the right: Add '-263440' to each side of the equation. 263440 + -1096x + -263440 + x2 = 0 + -263440 Reorder the terms: 263440 + -263440 + -1096x + x2 = 0 + -263440 Combine like terms: 263440 + -263440 = 0 0 + -1096x + x2 = 0 + -263440 -1096x + x2 = 0 + -263440 Combine like terms: 0 + -263440 = -263440 -1096x + x2 = -263440 The x term is -1096x. Take half its coefficient (-548). Square it (300304) and add it to both sides. Add '300304' to each side of the equation. -1096x + 300304 + x2 = -263440 + 300304 Reorder the terms: 300304 + -1096x + x2 = -263440 + 300304 Combine like terms: -263440 + 300304 = 36864 300304 + -1096x + x2 = 36864 Factor a perfect square on the left side: (x + -548)(x + -548) = 36864 Calculate the square root of the right side: 192 Break this problem into two subproblems by setting (x + -548) equal to 192 and -192.Subproblem 1
x + -548 = 192 Simplifying x + -548 = 192 Reorder the terms: -548 + x = 192 Solving -548 + x = 192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '548' to each side of the equation. -548 + 548 + x = 192 + 548 Combine like terms: -548 + 548 = 0 0 + x = 192 + 548 x = 192 + 548 Combine like terms: 192 + 548 = 740 x = 740 Simplifying x = 740Subproblem 2
x + -548 = -192 Simplifying x + -548 = -192 Reorder the terms: -548 + x = -192 Solving -548 + x = -192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '548' to each side of the equation. -548 + 548 + x = -192 + 548 Combine like terms: -548 + 548 = 0 0 + x = -192 + 548 x = -192 + 548 Combine like terms: -192 + 548 = 356 x = 356 Simplifying x = 356Solution
The solution to the problem is based on the solutions from the subproblems. x = {740, 356}
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