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Simplifying x2 + x + -304 = 0 Reorder the terms: -304 + x + x2 = 0 Solving -304 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '304' to each side of the equation. -304 + x + 304 + x2 = 0 + 304 Reorder the terms: -304 + 304 + x + x2 = 0 + 304 Combine like terms: -304 + 304 = 0 0 + x + x2 = 0 + 304 x + x2 = 0 + 304 Combine like terms: 0 + 304 = 304 x + x2 = 304 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 = 304 + 0.25 Reorder the terms: 0.25 + x + x2 = 304 + 0.25 Combine like terms: 304 + 0.25 = 304.25 0.25 + x + x2 = 304.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 304.25 Calculate the square root of the right side: 17.442763543 Break this problem into two subproblems by setting (x + 0.5) equal to 17.442763543 and -17.442763543.Subproblem 1
x + 0.5 = 17.442763543 Simplifying x + 0.5 = 17.442763543 Reorder the terms: 0.5 + x = 17.442763543 Solving 0.5 + x = 17.442763543 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 = 17.442763543 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 17.442763543 + -0.5 x = 17.442763543 + -0.5 Combine like terms: 17.442763543 + -0.5 = 16.942763543 x = 16.942763543 Simplifying x = 16.942763543Subproblem 2
x + 0.5 = -17.442763543 Simplifying x + 0.5 = -17.442763543 Reorder the terms: 0.5 + x = -17.442763543 Solving 0.5 + x = -17.442763543 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 = -17.442763543 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -17.442763543 + -0.5 x = -17.442763543 + -0.5 Combine like terms: -17.442763543 + -0.5 = -17.942763543 x = -17.942763543 Simplifying x = -17.942763543Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.942763543, -17.942763543}
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