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Simplifying x2 + 4x = 900 Reorder the terms: 4x + x2 = 900 Solving 4x + x2 = 900 Solving for variable 'x'. Reorder the terms: -900 + 4x + x2 = 900 + -900 Combine like terms: 900 + -900 = 0 -900 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '900' to each side of the equation. -900 + 4x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + 4x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 4x + x2 = 0 + 900 4x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 4x + x2 = 900 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 900 + 4 Reorder the terms: 4 + 4x + x2 = 900 + 4 Combine like terms: 900 + 4 = 904 4 + 4x + x2 = 904 Factor a perfect square on the left side: (x + 2)(x + 2) = 904 Calculate the square root of the right side: 30.066592757 Break this problem into two subproblems by setting (x + 2) equal to 30.066592757 and -30.066592757.Subproblem 1
x + 2 = 30.066592757 Simplifying x + 2 = 30.066592757 Reorder the terms: 2 + x = 30.066592757 Solving 2 + x = 30.066592757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 30.066592757 + -2 Combine like terms: 2 + -2 = 0 0 + x = 30.066592757 + -2 x = 30.066592757 + -2 Combine like terms: 30.066592757 + -2 = 28.066592757 x = 28.066592757 Simplifying x = 28.066592757Subproblem 2
x + 2 = -30.066592757 Simplifying x + 2 = -30.066592757 Reorder the terms: 2 + x = -30.066592757 Solving 2 + x = -30.066592757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -30.066592757 + -2 Combine like terms: 2 + -2 = 0 0 + x = -30.066592757 + -2 x = -30.066592757 + -2 Combine like terms: -30.066592757 + -2 = -32.066592757 x = -32.066592757 Simplifying x = -32.066592757Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.066592757, -32.066592757}
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