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Simplifying x2 + 2x = 57.3 Reorder the terms: 2x + x2 = 57.3 Solving 2x + x2 = 57.3 Solving for variable 'x'. Reorder the terms: -57.3 + 2x + x2 = 57.3 + -57.3 Combine like terms: 57.3 + -57.3 = 0.0 -57.3 + 2x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '57.3' to each side of the equation. -57.3 + 2x + 57.3 + x2 = 0.0 + 57.3 Reorder the terms: -57.3 + 57.3 + 2x + x2 = 0.0 + 57.3 Combine like terms: -57.3 + 57.3 = 0.0 0.0 + 2x + x2 = 0.0 + 57.3 2x + x2 = 0.0 + 57.3 Combine like terms: 0.0 + 57.3 = 57.3 2x + x2 = 57.3 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 = 57.3 + 1 Reorder the terms: 1 + 2x + x2 = 57.3 + 1 Combine like terms: 57.3 + 1 = 58.3 1 + 2x + x2 = 58.3 Factor a perfect square on the left side: (x + 1)(x + 1) = 58.3 Calculate the square root of the right side: 7.635443668 Break this problem into two subproblems by setting (x + 1) equal to 7.635443668 and -7.635443668.Subproblem 1
x + 1 = 7.635443668 Simplifying x + 1 = 7.635443668 Reorder the terms: 1 + x = 7.635443668 Solving 1 + x = 7.635443668 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 = 7.635443668 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.635443668 + -1 x = 7.635443668 + -1 Combine like terms: 7.635443668 + -1 = 6.635443668 x = 6.635443668 Simplifying x = 6.635443668Subproblem 2
x + 1 = -7.635443668 Simplifying x + 1 = -7.635443668 Reorder the terms: 1 + x = -7.635443668 Solving 1 + x = -7.635443668 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 = -7.635443668 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.635443668 + -1 x = -7.635443668 + -1 Combine like terms: -7.635443668 + -1 = -8.635443668 x = -8.635443668 Simplifying x = -8.635443668Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.635443668, -8.635443668}
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