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Simplifying x2 + -3x + -34 = 0 Reorder the terms: -34 + -3x + x2 = 0 Solving -34 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + -3x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + -3x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -3x + x2 = 0 + 34 -3x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 -3x + x2 = 34 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 = 34 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 34 + 2.25 Combine like terms: 34 + 2.25 = 36.25 2.25 + -3x + x2 = 36.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + -1.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + -1.5 = 6.020797289 Simplifying x + -1.5 = 6.020797289 Reorder the terms: -1.5 + x = 6.020797289 Solving -1.5 + x = 6.020797289 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 = 6.020797289 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.020797289 + 1.5 x = 6.020797289 + 1.5 Combine like terms: 6.020797289 + 1.5 = 7.520797289 x = 7.520797289 Simplifying x = 7.520797289Subproblem 2
x + -1.5 = -6.020797289 Simplifying x + -1.5 = -6.020797289 Reorder the terms: -1.5 + x = -6.020797289 Solving -1.5 + x = -6.020797289 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 = -6.020797289 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.020797289 + 1.5 x = -6.020797289 + 1.5 Combine like terms: -6.020797289 + 1.5 = -4.520797289 x = -4.520797289 Simplifying x = -4.520797289Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.520797289, -4.520797289}
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