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Simplifying x2 + 3x = 900 Reorder the terms: 3x + x2 = 900 Solving 3x + x2 = 900 Solving for variable 'x'. Reorder the terms: -900 + 3x + x2 = 900 + -900 Combine like terms: 900 + -900 = 0 -900 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '900' to each side of the equation. -900 + 3x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + 3x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 3x + x2 = 0 + 900 3x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 3x + x2 = 900 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 = 900 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 900 + 2.25 Combine like terms: 900 + 2.25 = 902.25 2.25 + 3x + x2 = 902.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 902.25 Calculate the square root of the right side: 30.037476592 Break this problem into two subproblems by setting (x + 1.5) equal to 30.037476592 and -30.037476592.Subproblem 1
x + 1.5 = 30.037476592 Simplifying x + 1.5 = 30.037476592 Reorder the terms: 1.5 + x = 30.037476592 Solving 1.5 + x = 30.037476592 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 = 30.037476592 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 30.037476592 + -1.5 x = 30.037476592 + -1.5 Combine like terms: 30.037476592 + -1.5 = 28.537476592 x = 28.537476592 Simplifying x = 28.537476592Subproblem 2
x + 1.5 = -30.037476592 Simplifying x + 1.5 = -30.037476592 Reorder the terms: 1.5 + x = -30.037476592 Solving 1.5 + x = -30.037476592 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 = -30.037476592 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -30.037476592 + -1.5 x = -30.037476592 + -1.5 Combine like terms: -30.037476592 + -1.5 = -31.537476592 x = -31.537476592 Simplifying x = -31.537476592Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.537476592, -31.537476592}
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