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Simplifying x2 + 3x + -718 = 0 Reorder the terms: -718 + 3x + x2 = 0 Solving -718 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '718' to each side of the equation. -718 + 3x + 718 + x2 = 0 + 718 Reorder the terms: -718 + 718 + 3x + x2 = 0 + 718 Combine like terms: -718 + 718 = 0 0 + 3x + x2 = 0 + 718 3x + x2 = 0 + 718 Combine like terms: 0 + 718 = 718 3x + x2 = 718 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 = 718 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 718 + 2.25 Combine like terms: 718 + 2.25 = 720.25 2.25 + 3x + x2 = 720.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 720.25 Calculate the square root of the right side: 26.837473801 Break this problem into two subproblems by setting (x + 1.5) equal to 26.837473801 and -26.837473801.Subproblem 1
x + 1.5 = 26.837473801 Simplifying x + 1.5 = 26.837473801 Reorder the terms: 1.5 + x = 26.837473801 Solving 1.5 + x = 26.837473801 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 = 26.837473801 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 26.837473801 + -1.5 x = 26.837473801 + -1.5 Combine like terms: 26.837473801 + -1.5 = 25.337473801 x = 25.337473801 Simplifying x = 25.337473801Subproblem 2
x + 1.5 = -26.837473801 Simplifying x + 1.5 = -26.837473801 Reorder the terms: 1.5 + x = -26.837473801 Solving 1.5 + x = -26.837473801 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 = -26.837473801 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -26.837473801 + -1.5 x = -26.837473801 + -1.5 Combine like terms: -26.837473801 + -1.5 = -28.337473801 x = -28.337473801 Simplifying x = -28.337473801Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.337473801, -28.337473801}
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