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Simplifying 57 = (x + 2) * x Reorder the terms: 57 = (2 + x) * x Reorder the terms for easier multiplication: 57 = x(2 + x) 57 = (2 * x + x * x) 57 = (2x + x2) Solving 57 = 2x + x2 Solving for variable 'x'. Reorder the terms: 57 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 57 + -2x + -1x2 = 0 + x2 + -1x2 57 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 57 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -57 + 2x + x2 = 0 Move the constant term to the right: Add '57' to each side of the equation. -57 + 2x + 57 + x2 = 0 + 57 Reorder the terms: -57 + 57 + 2x + x2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + 2x + x2 = 0 + 57 2x + x2 = 0 + 57 Combine like terms: 0 + 57 = 57 2x + x2 = 57 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 57 + 1 Reorder the terms: 1 + 2x + x2 = 57 + 1 Combine like terms: 57 + 1 = 58 1 + 2x + x2 = 58 Factor a perfect square on the left side: (x + 1)(x + 1) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + 1) equal to 7.615773106 and -7.615773106.Subproblem 1
x + 1 = 7.615773106 Simplifying x + 1 = 7.615773106 Reorder the terms: 1 + x = 7.615773106 Solving 1 + x = 7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 7.615773106 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.615773106 + -1 x = 7.615773106 + -1 Combine like terms: 7.615773106 + -1 = 6.615773106 x = 6.615773106 Simplifying x = 6.615773106Subproblem 2
x + 1 = -7.615773106 Simplifying x + 1 = -7.615773106 Reorder the terms: 1 + x = -7.615773106 Solving 1 + x = -7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -7.615773106 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.615773106 + -1 x = -7.615773106 + -1 Combine like terms: -7.615773106 + -1 = -8.615773106 x = -8.615773106 Simplifying x = -8.615773106Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.615773106, -8.615773106}
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