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Simplifying x2 + 63x + -51000 = 0 Reorder the terms: -51000 + 63x + x2 = 0 Solving -51000 + 63x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '51000' to each side of the equation. -51000 + 63x + 51000 + x2 = 0 + 51000 Reorder the terms: -51000 + 51000 + 63x + x2 = 0 + 51000 Combine like terms: -51000 + 51000 = 0 0 + 63x + x2 = 0 + 51000 63x + x2 = 0 + 51000 Combine like terms: 0 + 51000 = 51000 63x + x2 = 51000 The x term is 63x. Take half its coefficient (31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. 63x + 992.25 + x2 = 51000 + 992.25 Reorder the terms: 992.25 + 63x + x2 = 51000 + 992.25 Combine like terms: 51000 + 992.25 = 51992.25 992.25 + 63x + x2 = 51992.25 Factor a perfect square on the left side: (x + 31.5)(x + 31.5) = 51992.25 Calculate the square root of the right side: 228.018091388 Break this problem into two subproblems by setting (x + 31.5) equal to 228.018091388 and -228.018091388.Subproblem 1
x + 31.5 = 228.018091388 Simplifying x + 31.5 = 228.018091388 Reorder the terms: 31.5 + x = 228.018091388 Solving 31.5 + x = 228.018091388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = 228.018091388 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = 228.018091388 + -31.5 x = 228.018091388 + -31.5 Combine like terms: 228.018091388 + -31.5 = 196.518091388 x = 196.518091388 Simplifying x = 196.518091388Subproblem 2
x + 31.5 = -228.018091388 Simplifying x + 31.5 = -228.018091388 Reorder the terms: 31.5 + x = -228.018091388 Solving 31.5 + x = -228.018091388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = -228.018091388 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = -228.018091388 + -31.5 x = -228.018091388 + -31.5 Combine like terms: -228.018091388 + -31.5 = -259.518091388 x = -259.518091388 Simplifying x = -259.518091388Solution
The solution to the problem is based on the solutions from the subproblems. x = {196.518091388, -259.518091388}
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