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Simplifying x2 + x + -3900 = 0 Reorder the terms: -3900 + x + x2 = 0 Solving -3900 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3900' to each side of the equation. -3900 + x + 3900 + x2 = 0 + 3900 Reorder the terms: -3900 + 3900 + x + x2 = 0 + 3900 Combine like terms: -3900 + 3900 = 0 0 + x + x2 = 0 + 3900 x + x2 = 0 + 3900 Combine like terms: 0 + 3900 = 3900 x + x2 = 3900 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 3900 + 0.25 Reorder the terms: 0.25 + x + x2 = 3900 + 0.25 Combine like terms: 3900 + 0.25 = 3900.25 0.25 + x + x2 = 3900.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3900.25 Calculate the square root of the right side: 62.451981554 Break this problem into two subproblems by setting (x + 0.5) equal to 62.451981554 and -62.451981554.Subproblem 1
x + 0.5 = 62.451981554 Simplifying x + 0.5 = 62.451981554 Reorder the terms: 0.5 + x = 62.451981554 Solving 0.5 + x = 62.451981554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 62.451981554 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 62.451981554 + -0.5 x = 62.451981554 + -0.5 Combine like terms: 62.451981554 + -0.5 = 61.951981554 x = 61.951981554 Simplifying x = 61.951981554Subproblem 2
x + 0.5 = -62.451981554 Simplifying x + 0.5 = -62.451981554 Reorder the terms: 0.5 + x = -62.451981554 Solving 0.5 + x = -62.451981554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -62.451981554 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -62.451981554 + -0.5 x = -62.451981554 + -0.5 Combine like terms: -62.451981554 + -0.5 = -62.951981554 x = -62.951981554 Simplifying x = -62.951981554Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.951981554, -62.951981554}
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