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Simplifying x2 + 3x + -729 = 0 Reorder the terms: -729 + 3x + x2 = 0 Solving -729 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '729' to each side of the equation. -729 + 3x + 729 + x2 = 0 + 729 Reorder the terms: -729 + 729 + 3x + x2 = 0 + 729 Combine like terms: -729 + 729 = 0 0 + 3x + x2 = 0 + 729 3x + x2 = 0 + 729 Combine like terms: 0 + 729 = 729 3x + x2 = 729 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 = 729 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 729 + 2.25 Combine like terms: 729 + 2.25 = 731.25 2.25 + 3x + x2 = 731.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 731.25 Calculate the square root of the right side: 27.041634566 Break this problem into two subproblems by setting (x + 1.5) equal to 27.041634566 and -27.041634566.Subproblem 1
x + 1.5 = 27.041634566 Simplifying x + 1.5 = 27.041634566 Reorder the terms: 1.5 + x = 27.041634566 Solving 1.5 + x = 27.041634566 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 = 27.041634566 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 27.041634566 + -1.5 x = 27.041634566 + -1.5 Combine like terms: 27.041634566 + -1.5 = 25.541634566 x = 25.541634566 Simplifying x = 25.541634566Subproblem 2
x + 1.5 = -27.041634566 Simplifying x + 1.5 = -27.041634566 Reorder the terms: 1.5 + x = -27.041634566 Solving 1.5 + x = -27.041634566 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 = -27.041634566 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -27.041634566 + -1.5 x = -27.041634566 + -1.5 Combine like terms: -27.041634566 + -1.5 = -28.541634566 x = -28.541634566 Simplifying x = -28.541634566Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.541634566, -28.541634566}
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