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Simplifying x + 2x2 + -57 = 0 Reorder the terms: -57 + x + 2x2 = 0 Solving -57 + x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -28.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '28.5' to each side of the equation. -28.5 + 0.5x + 28.5 + x2 = 0 + 28.5 Reorder the terms: -28.5 + 28.5 + 0.5x + x2 = 0 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + 0.5x + x2 = 0 + 28.5 0.5x + x2 = 0 + 28.5 Combine like terms: 0 + 28.5 = 28.5 0.5x + x2 = 28.5 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. 0.5x + 0.25 + x2 = 28.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 28.5 + 0.25 Combine like terms: 28.5 + 0.25 = 28.75 0.25 + 0.5x + x2 = 28.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 28.75 Calculate the square root of the right side: 5.361902647 Break this problem into two subproblems by setting (x + 0.5) equal to 5.361902647 and -5.361902647.Subproblem 1
x + 0.5 = 5.361902647 Simplifying x + 0.5 = 5.361902647 Reorder the terms: 0.5 + x = 5.361902647 Solving 0.5 + x = 5.361902647 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 = 5.361902647 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.361902647 + -0.5 x = 5.361902647 + -0.5 Combine like terms: 5.361902647 + -0.5 = 4.861902647 x = 4.861902647 Simplifying x = 4.861902647Subproblem 2
x + 0.5 = -5.361902647 Simplifying x + 0.5 = -5.361902647 Reorder the terms: 0.5 + x = -5.361902647 Solving 0.5 + x = -5.361902647 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 = -5.361902647 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.361902647 + -0.5 x = -5.361902647 + -0.5 Combine like terms: -5.361902647 + -0.5 = -5.861902647 x = -5.861902647 Simplifying x = -5.861902647Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.861902647, -5.861902647}
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