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Simplifying x + 3 = 224x2 Reorder the terms: 3 + x = 224x2 Solving 3 + x = 224x2 Solving for variable 'x'. Combine like terms: 224x2 + -224x2 = 0 3 + x + -224x2 = 0 Begin completing the square. Divide all terms by -224 the coefficient of the squared term: Divide each side by '-224'. -0.01339285714 + -0.004464285714x + x2 = 0 Move the constant term to the right: Add '0.01339285714' to each side of the equation. -0.01339285714 + -0.004464285714x + 0.01339285714 + x2 = 0 + 0.01339285714 Reorder the terms: -0.01339285714 + 0.01339285714 + -0.004464285714x + x2 = 0 + 0.01339285714 Combine like terms: -0.01339285714 + 0.01339285714 = 0.00000000000 0.00000000000 + -0.004464285714x + x2 = 0 + 0.01339285714 -0.004464285714x + x2 = 0 + 0.01339285714 Combine like terms: 0 + 0.01339285714 = 0.01339285714 -0.004464285714x + x2 = 0.01339285714 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. -0.004464285714x + 0.25 + x2 = 0.01339285714 + 0.25 Reorder the terms: 0.25 + -0.004464285714x + x2 = 0.01339285714 + 0.25 Combine like terms: 0.01339285714 + 0.25 = 0.26339285714 0.25 + -0.004464285714x + x2 = 0.26339285714 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.26339285714 Calculate the square root of the right side: 0.513218138 Break this problem into two subproblems by setting (x + 0.5) equal to 0.513218138 and -0.513218138.Subproblem 1
x + 0.5 = 0.513218138 Simplifying x + 0.5 = 0.513218138 Reorder the terms: 0.5 + x = 0.513218138 Solving 0.5 + x = 0.513218138 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 = 0.513218138 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.513218138 + -0.5 x = 0.513218138 + -0.5 Combine like terms: 0.513218138 + -0.5 = 0.013218138 x = 0.013218138 Simplifying x = 0.013218138Subproblem 2
x + 0.5 = -0.513218138 Simplifying x + 0.5 = -0.513218138 Reorder the terms: 0.5 + x = -0.513218138 Solving 0.5 + x = -0.513218138 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 = -0.513218138 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.513218138 + -0.5 x = -0.513218138 + -0.5 Combine like terms: -0.513218138 + -0.5 = -1.013218138 x = -1.013218138 Simplifying x = -1.013218138Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.013218138, -1.013218138}
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