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Simplifying x2 + 3x + -3600 = 0 Reorder the terms: -3600 + 3x + x2 = 0 Solving -3600 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + 3x + 3600 + x2 = 0 + 3600 Reorder the terms: -3600 + 3600 + 3x + x2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + 3x + x2 = 0 + 3600 3x + x2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 3x + x2 = 3600 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 = 3600 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 3600 + 2.25 Combine like terms: 3600 + 2.25 = 3602.25 2.25 + 3x + x2 = 3602.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3602.25 Calculate the square root of the right side: 60.018747071 Break this problem into two subproblems by setting (x + 1.5) equal to 60.018747071 and -60.018747071.Subproblem 1
x + 1.5 = 60.018747071 Simplifying x + 1.5 = 60.018747071 Reorder the terms: 1.5 + x = 60.018747071 Solving 1.5 + x = 60.018747071 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 = 60.018747071 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 60.018747071 + -1.5 x = 60.018747071 + -1.5 Combine like terms: 60.018747071 + -1.5 = 58.518747071 x = 58.518747071 Simplifying x = 58.518747071Subproblem 2
x + 1.5 = -60.018747071 Simplifying x + 1.5 = -60.018747071 Reorder the terms: 1.5 + x = -60.018747071 Solving 1.5 + x = -60.018747071 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 = -60.018747071 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -60.018747071 + -1.5 x = -60.018747071 + -1.5 Combine like terms: -60.018747071 + -1.5 = -61.518747071 x = -61.518747071 Simplifying x = -61.518747071Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.518747071, -61.518747071}
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