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Simplifying 0.68 = x + x2 Solving 0.68 = x + x2 Solving for variable 'x'. Reorder the terms: 0.68 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 0.68 + -1x + -1x2 = 0 + x2 + -1x2 0.68 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.68 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.68 + x + x2 = 0 Move the constant term to the right: Add '0.68' to each side of the equation. -0.68 + x + 0.68 + x2 = 0 + 0.68 Reorder the terms: -0.68 + 0.68 + x + x2 = 0 + 0.68 Combine like terms: -0.68 + 0.68 = 0.00 0.00 + x + x2 = 0 + 0.68 x + x2 = 0 + 0.68 Combine like terms: 0 + 0.68 = 0.68 x + x2 = 0.68 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. + 0.25 + x2 = 0.68 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.68 + 0.25 Combine like terms: 0.68 + 0.25 = 0.93 1.25 + x2 = 0.93 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.93 Calculate the square root of the right side: 0.964365076 Break this problem into two subproblems by setting (x + 0.5) equal to 0.964365076 and -0.964365076.Subproblem 1
x + 0.5 = 0.964365076 Simplifying x + 0.5 = 0.964365076 Reorder the terms: 0.5 + x = 0.964365076 Solving 0.5 + x = 0.964365076 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 = 0.964365076 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.964365076 + -0.5 x = 0.964365076 + -0.5 Combine like terms: 0.964365076 + -0.5 = 0.464365076 x = 0.464365076 Simplifying x = 0.464365076Subproblem 2
x + 0.5 = -0.964365076 Simplifying x + 0.5 = -0.964365076 Reorder the terms: 0.5 + x = -0.964365076 Solving 0.5 + x = -0.964365076 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 = -0.964365076 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.964365076 + -0.5 x = -0.964365076 + -0.5 Combine like terms: -0.964365076 + -0.5 = -1.464365076 x = -1.464365076 Simplifying x = -1.464365076Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.464365076, -1.464365076}
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