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Simplifying x2 + 3x + -69 = 0 Reorder the terms: -69 + 3x + x2 = 0 Solving -69 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + 3x + 69 + x2 = 0 + 69 Reorder the terms: -69 + 69 + 3x + x2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + 3x + x2 = 0 + 69 3x + x2 = 0 + 69 Combine like terms: 0 + 69 = 69 3x + x2 = 69 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 = 69 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 69 + 2.25 Combine like terms: 69 + 2.25 = 71.25 2.25 + 3x + x2 = 71.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 71.25 Calculate the square root of the right side: 8.440971508 Break this problem into two subproblems by setting (x + 1.5) equal to 8.440971508 and -8.440971508.Subproblem 1
x + 1.5 = 8.440971508 Simplifying x + 1.5 = 8.440971508 Reorder the terms: 1.5 + x = 8.440971508 Solving 1.5 + x = 8.440971508 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 = 8.440971508 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.440971508 + -1.5 x = 8.440971508 + -1.5 Combine like terms: 8.440971508 + -1.5 = 6.940971508 x = 6.940971508 Simplifying x = 6.940971508Subproblem 2
x + 1.5 = -8.440971508 Simplifying x + 1.5 = -8.440971508 Reorder the terms: 1.5 + x = -8.440971508 Solving 1.5 + x = -8.440971508 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 = -8.440971508 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.440971508 + -1.5 x = -8.440971508 + -1.5 Combine like terms: -8.440971508 + -1.5 = -9.940971508 x = -9.940971508 Simplifying x = -9.940971508Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.940971508, -9.940971508}
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