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Simplifying x2 + 3x + -600 = 0 Reorder the terms: -600 + 3x + x2 = 0 Solving -600 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + 3x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + 3x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + 3x + x2 = 0 + 600 3x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 3x + x2 = 600 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 = 600 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 600 + 2.25 Combine like terms: 600 + 2.25 = 602.25 2.25 + 3x + x2 = 602.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 602.25 Calculate the square root of the right side: 24.540782384 Break this problem into two subproblems by setting (x + 1.5) equal to 24.540782384 and -24.540782384.Subproblem 1
x + 1.5 = 24.540782384 Simplifying x + 1.5 = 24.540782384 Reorder the terms: 1.5 + x = 24.540782384 Solving 1.5 + x = 24.540782384 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 = 24.540782384 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 24.540782384 + -1.5 x = 24.540782384 + -1.5 Combine like terms: 24.540782384 + -1.5 = 23.040782384 x = 23.040782384 Simplifying x = 23.040782384Subproblem 2
x + 1.5 = -24.540782384 Simplifying x + 1.5 = -24.540782384 Reorder the terms: 1.5 + x = -24.540782384 Solving 1.5 + x = -24.540782384 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 = -24.540782384 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -24.540782384 + -1.5 x = -24.540782384 + -1.5 Combine like terms: -24.540782384 + -1.5 = -26.040782384 x = -26.040782384 Simplifying x = -26.040782384Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.040782384, -26.040782384}
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