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Simplifying -1x2 + 150x + -5200 = 0 Reorder the terms: -5200 + 150x + -1x2 = 0 Solving -5200 + 150x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5200 + -150x + x2 = 0 Move the constant term to the right: Add '-5200' to each side of the equation. 5200 + -150x + -5200 + x2 = 0 + -5200 Reorder the terms: 5200 + -5200 + -150x + x2 = 0 + -5200 Combine like terms: 5200 + -5200 = 0 0 + -150x + x2 = 0 + -5200 -150x + x2 = 0 + -5200 Combine like terms: 0 + -5200 = -5200 -150x + x2 = -5200 The x term is -150x. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150x + 5625 + x2 = -5200 + 5625 Reorder the terms: 5625 + -150x + x2 = -5200 + 5625 Combine like terms: -5200 + 5625 = 425 5625 + -150x + x2 = 425 Factor a perfect square on the left side: (x + -75)(x + -75) = 425 Calculate the square root of the right side: 20.615528128 Break this problem into two subproblems by setting (x + -75) equal to 20.615528128 and -20.615528128.Subproblem 1
x + -75 = 20.615528128 Simplifying x + -75 = 20.615528128 Reorder the terms: -75 + x = 20.615528128 Solving -75 + x = 20.615528128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = 20.615528128 + 75 Combine like terms: -75 + 75 = 0 0 + x = 20.615528128 + 75 x = 20.615528128 + 75 Combine like terms: 20.615528128 + 75 = 95.615528128 x = 95.615528128 Simplifying x = 95.615528128Subproblem 2
x + -75 = -20.615528128 Simplifying x + -75 = -20.615528128 Reorder the terms: -75 + x = -20.615528128 Solving -75 + x = -20.615528128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = -20.615528128 + 75 Combine like terms: -75 + 75 = 0 0 + x = -20.615528128 + 75 x = -20.615528128 + 75 Combine like terms: -20.615528128 + 75 = 54.384471872 x = 54.384471872 Simplifying x = 54.384471872Solution
The solution to the problem is based on the solutions from the subproblems. x = {95.615528128, 54.384471872}
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