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Simplifying x2 + 4x = 930 Reorder the terms: 4x + x2 = 930 Solving 4x + x2 = 930 Solving for variable 'x'. Reorder the terms: -930 + 4x + x2 = 930 + -930 Combine like terms: 930 + -930 = 0 -930 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '930' to each side of the equation. -930 + 4x + 930 + x2 = 0 + 930 Reorder the terms: -930 + 930 + 4x + x2 = 0 + 930 Combine like terms: -930 + 930 = 0 0 + 4x + x2 = 0 + 930 4x + x2 = 0 + 930 Combine like terms: 0 + 930 = 930 4x + x2 = 930 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 = 930 + 4 Reorder the terms: 4 + 4x + x2 = 930 + 4 Combine like terms: 930 + 4 = 934 4 + 4x + x2 = 934 Factor a perfect square on the left side: (x + 2)(x + 2) = 934 Calculate the square root of the right side: 30.56141358 Break this problem into two subproblems by setting (x + 2) equal to 30.56141358 and -30.56141358.Subproblem 1
x + 2 = 30.56141358 Simplifying x + 2 = 30.56141358 Reorder the terms: 2 + x = 30.56141358 Solving 2 + x = 30.56141358 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 = 30.56141358 + -2 Combine like terms: 2 + -2 = 0 0 + x = 30.56141358 + -2 x = 30.56141358 + -2 Combine like terms: 30.56141358 + -2 = 28.56141358 x = 28.56141358 Simplifying x = 28.56141358Subproblem 2
x + 2 = -30.56141358 Simplifying x + 2 = -30.56141358 Reorder the terms: 2 + x = -30.56141358 Solving 2 + x = -30.56141358 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 = -30.56141358 + -2 Combine like terms: 2 + -2 = 0 0 + x = -30.56141358 + -2 x = -30.56141358 + -2 Combine like terms: -30.56141358 + -2 = -32.56141358 x = -32.56141358 Simplifying x = -32.56141358Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.56141358, -32.56141358}
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