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Simplifying x2 + 3x + -7140 = 0 Reorder the terms: -7140 + 3x + x2 = 0 Solving -7140 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7140' to each side of the equation. -7140 + 3x + 7140 + x2 = 0 + 7140 Reorder the terms: -7140 + 7140 + 3x + x2 = 0 + 7140 Combine like terms: -7140 + 7140 = 0 0 + 3x + x2 = 0 + 7140 3x + x2 = 0 + 7140 Combine like terms: 0 + 7140 = 7140 3x + x2 = 7140 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 = 7140 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 7140 + 2.25 Combine like terms: 7140 + 2.25 = 7142.25 2.25 + 3x + x2 = 7142.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 7142.25 Calculate the square root of the right side: 84.511833491 Break this problem into two subproblems by setting (x + 1.5) equal to 84.511833491 and -84.511833491.Subproblem 1
x + 1.5 = 84.511833491 Simplifying x + 1.5 = 84.511833491 Reorder the terms: 1.5 + x = 84.511833491 Solving 1.5 + x = 84.511833491 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 = 84.511833491 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 84.511833491 + -1.5 x = 84.511833491 + -1.5 Combine like terms: 84.511833491 + -1.5 = 83.011833491 x = 83.011833491 Simplifying x = 83.011833491Subproblem 2
x + 1.5 = -84.511833491 Simplifying x + 1.5 = -84.511833491 Reorder the terms: 1.5 + x = -84.511833491 Solving 1.5 + x = -84.511833491 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 = -84.511833491 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -84.511833491 + -1.5 x = -84.511833491 + -1.5 Combine like terms: -84.511833491 + -1.5 = -86.011833491 x = -86.011833491 Simplifying x = -86.011833491Solution
The solution to the problem is based on the solutions from the subproblems. x = {83.011833491, -86.011833491}
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