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Simplifying x2 + 150x + -8400 = 0 Reorder the terms: -8400 + 150x + x2 = 0 Solving -8400 + 150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8400' to each side of the equation. -8400 + 150x + 8400 + x2 = 0 + 8400 Reorder the terms: -8400 + 8400 + 150x + x2 = 0 + 8400 Combine like terms: -8400 + 8400 = 0 0 + 150x + x2 = 0 + 8400 150x + x2 = 0 + 8400 Combine like terms: 0 + 8400 = 8400 150x + x2 = 8400 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 = 8400 + 5625 Reorder the terms: 5625 + 150x + x2 = 8400 + 5625 Combine like terms: 8400 + 5625 = 14025 5625 + 150x + x2 = 14025 Factor a perfect square on the left side: (x + 75)(x + 75) = 14025 Calculate the square root of the right side: 118.427192823 Break this problem into two subproblems by setting (x + 75) equal to 118.427192823 and -118.427192823.Subproblem 1
x + 75 = 118.427192823 Simplifying x + 75 = 118.427192823 Reorder the terms: 75 + x = 118.427192823 Solving 75 + x = 118.427192823 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 = 118.427192823 + -75 Combine like terms: 75 + -75 = 0 0 + x = 118.427192823 + -75 x = 118.427192823 + -75 Combine like terms: 118.427192823 + -75 = 43.427192823 x = 43.427192823 Simplifying x = 43.427192823Subproblem 2
x + 75 = -118.427192823 Simplifying x + 75 = -118.427192823 Reorder the terms: 75 + x = -118.427192823 Solving 75 + x = -118.427192823 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 = -118.427192823 + -75 Combine like terms: 75 + -75 = 0 0 + x = -118.427192823 + -75 x = -118.427192823 + -75 Combine like terms: -118.427192823 + -75 = -193.427192823 x = -193.427192823 Simplifying x = -193.427192823Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.427192823, -193.427192823}
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