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Simplifying x2 + 4x = 869 Reorder the terms: 4x + x2 = 869 Solving 4x + x2 = 869 Solving for variable 'x'. Reorder the terms: -869 + 4x + x2 = 869 + -869 Combine like terms: 869 + -869 = 0 -869 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '869' to each side of the equation. -869 + 4x + 869 + x2 = 0 + 869 Reorder the terms: -869 + 869 + 4x + x2 = 0 + 869 Combine like terms: -869 + 869 = 0 0 + 4x + x2 = 0 + 869 4x + x2 = 0 + 869 Combine like terms: 0 + 869 = 869 4x + x2 = 869 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 = 869 + 4 Reorder the terms: 4 + 4x + x2 = 869 + 4 Combine like terms: 869 + 4 = 873 4 + 4x + x2 = 873 Factor a perfect square on the left side: (x + 2)(x + 2) = 873 Calculate the square root of the right side: 29.546573405 Break this problem into two subproblems by setting (x + 2) equal to 29.546573405 and -29.546573405.Subproblem 1
x + 2 = 29.546573405 Simplifying x + 2 = 29.546573405 Reorder the terms: 2 + x = 29.546573405 Solving 2 + x = 29.546573405 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 = 29.546573405 + -2 Combine like terms: 2 + -2 = 0 0 + x = 29.546573405 + -2 x = 29.546573405 + -2 Combine like terms: 29.546573405 + -2 = 27.546573405 x = 27.546573405 Simplifying x = 27.546573405Subproblem 2
x + 2 = -29.546573405 Simplifying x + 2 = -29.546573405 Reorder the terms: 2 + x = -29.546573405 Solving 2 + x = -29.546573405 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 = -29.546573405 + -2 Combine like terms: 2 + -2 = 0 0 + x = -29.546573405 + -2 x = -29.546573405 + -2 Combine like terms: -29.546573405 + -2 = -31.546573405 x = -31.546573405 Simplifying x = -31.546573405Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.546573405, -31.546573405}
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