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Simplifying 1.12 = x(1 + x) 1.12 = (1 * x + x * x) 1.12 = (1x + x2) Solving 1.12 = 1x + x2 Solving for variable 'x'. Reorder the terms: 1.12 + -1x + -1x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 0 1.12 + -1x + -1x2 = 0 + x2 + -1x2 1.12 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1.12 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1.12 + x + x2 = 0 Move the constant term to the right: Add '1.12' to each side of the equation. -1.12 + x + 1.12 + x2 = 0 + 1.12 Reorder the terms: -1.12 + 1.12 + x + x2 = 0 + 1.12 Combine like terms: -1.12 + 1.12 = 0.00 0.00 + x + x2 = 0 + 1.12 x + x2 = 0 + 1.12 Combine like terms: 0 + 1.12 = 1.12 x + x2 = 1.12 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 = 1.12 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.12 + 0.25 Combine like terms: 1.12 + 0.25 = 1.37 1.25 + x2 = 1.37 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.37 Calculate the square root of the right side: 1.170469991 Break this problem into two subproblems by setting (x + 0.5) equal to 1.170469991 and -1.170469991.Subproblem 1
x + 0.5 = 1.170469991 Simplifying x + 0.5 = 1.170469991 Reorder the terms: 0.5 + x = 1.170469991 Solving 0.5 + x = 1.170469991 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 = 1.170469991 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.170469991 + -0.5 x = 1.170469991 + -0.5 Combine like terms: 1.170469991 + -0.5 = 0.670469991 x = 0.670469991 Simplifying x = 0.670469991Subproblem 2
x + 0.5 = -1.170469991 Simplifying x + 0.5 = -1.170469991 Reorder the terms: 0.5 + x = -1.170469991 Solving 0.5 + x = -1.170469991 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 = -1.170469991 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.170469991 + -0.5 x = -1.170469991 + -0.5 Combine like terms: -1.170469991 + -0.5 = -1.670469991 x = -1.670469991 Simplifying x = -1.670469991Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.670469991, -1.670469991}
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