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Simplifying -1.25x2 + 140x + -3000 = 0 Reorder the terms: -3000 + 140x + -1.25x2 = 0 Solving -3000 + 140x + -1.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.25 the coefficient of the squared term: Divide each side by '-1.25'. 2400 + -112x + x2 = 0 Move the constant term to the right: Add '-2400' to each side of the equation. 2400 + -112x + -2400 + x2 = 0 + -2400 Reorder the terms: 2400 + -2400 + -112x + x2 = 0 + -2400 Combine like terms: 2400 + -2400 = 0 0 + -112x + x2 = 0 + -2400 -112x + x2 = 0 + -2400 Combine like terms: 0 + -2400 = -2400 -112x + x2 = -2400 The x term is -112x. Take half its coefficient (-56). Square it (3136) and add it to both sides. Add '3136' to each side of the equation. -112x + 3136 + x2 = -2400 + 3136 Reorder the terms: 3136 + -112x + x2 = -2400 + 3136 Combine like terms: -2400 + 3136 = 736 3136 + -112x + x2 = 736 Factor a perfect square on the left side: (x + -56)(x + -56) = 736 Calculate the square root of the right side: 27.129319933 Break this problem into two subproblems by setting (x + -56) equal to 27.129319933 and -27.129319933.Subproblem 1
x + -56 = 27.129319933 Simplifying x + -56 = 27.129319933 Reorder the terms: -56 + x = 27.129319933 Solving -56 + x = 27.129319933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + x = 27.129319933 + 56 Combine like terms: -56 + 56 = 0 0 + x = 27.129319933 + 56 x = 27.129319933 + 56 Combine like terms: 27.129319933 + 56 = 83.129319933 x = 83.129319933 Simplifying x = 83.129319933Subproblem 2
x + -56 = -27.129319933 Simplifying x + -56 = -27.129319933 Reorder the terms: -56 + x = -27.129319933 Solving -56 + x = -27.129319933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + x = -27.129319933 + 56 Combine like terms: -56 + 56 = 0 0 + x = -27.129319933 + 56 x = -27.129319933 + 56 Combine like terms: -27.129319933 + 56 = 28.870680067 x = 28.870680067 Simplifying x = 28.870680067Solution
The solution to the problem is based on the solutions from the subproblems. x = {83.129319933, 28.870680067}
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