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Simplifying x2 + 21x + -50 = 0 Reorder the terms: -50 + 21x + x2 = 0 Solving -50 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 21x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 21x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 21x + x2 = 0 + 50 21x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 21x + x2 = 50 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = 50 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 50 + 110.25 Combine like terms: 50 + 110.25 = 160.25 110.25 + 21x + x2 = 160.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 160.25 Calculate the square root of the right side: 12.658988901 Break this problem into two subproblems by setting (x + 10.5) equal to 12.658988901 and -12.658988901.Subproblem 1
x + 10.5 = 12.658988901 Simplifying x + 10.5 = 12.658988901 Reorder the terms: 10.5 + x = 12.658988901 Solving 10.5 + x = 12.658988901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 12.658988901 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 12.658988901 + -10.5 x = 12.658988901 + -10.5 Combine like terms: 12.658988901 + -10.5 = 2.158988901 x = 2.158988901 Simplifying x = 2.158988901Subproblem 2
x + 10.5 = -12.658988901 Simplifying x + 10.5 = -12.658988901 Reorder the terms: 10.5 + x = -12.658988901 Solving 10.5 + x = -12.658988901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -12.658988901 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -12.658988901 + -10.5 x = -12.658988901 + -10.5 Combine like terms: -12.658988901 + -10.5 = -23.158988901 x = -23.158988901 Simplifying x = -23.158988901Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.158988901, -23.158988901}
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