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Simplifying x2 + 3x + -99 = 0 Reorder the terms: -99 + 3x + x2 = 0 Solving -99 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 3x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + 3x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 3x + x2 = 0 + 99 3x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 3x + x2 = 99 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 99 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 99 + 2.25 Combine like terms: 99 + 2.25 = 101.25 2.25 + 3x + x2 = 101.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 101.25 Calculate the square root of the right side: 10.062305899 Break this problem into two subproblems by setting (x + 1.5) equal to 10.062305899 and -10.062305899.Subproblem 1
x + 1.5 = 10.062305899 Simplifying x + 1.5 = 10.062305899 Reorder the terms: 1.5 + x = 10.062305899 Solving 1.5 + x = 10.062305899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 10.062305899 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.062305899 + -1.5 x = 10.062305899 + -1.5 Combine like terms: 10.062305899 + -1.5 = 8.562305899 x = 8.562305899 Simplifying x = 8.562305899Subproblem 2
x + 1.5 = -10.062305899 Simplifying x + 1.5 = -10.062305899 Reorder the terms: 1.5 + x = -10.062305899 Solving 1.5 + x = -10.062305899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -10.062305899 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.062305899 + -1.5 x = -10.062305899 + -1.5 Combine like terms: -10.062305899 + -1.5 = -11.562305899 x = -11.562305899 Simplifying x = -11.562305899Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.562305899, -11.562305899}
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