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Simplifying 2x + -1(x * x) = 0.1 Multiply x * x 2x + -1(x2) = 0.1 Solving 2x + -1x2 = 0.1 Solving for variable 'x'. Reorder the terms: -0.1 + 2x + -1x2 = 0.1 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 -0.1 + 2x + -1x2 = 0.0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.1 + -2x + x2 = 0.0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + -2x + -0.1 + x2 = 0.0 + -0.1 Reorder the terms: 0.1 + -0.1 + -2x + x2 = 0.0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + -2x + x2 = 0.0 + -0.1 -2x + x2 = 0.0 + -0.1 Combine like terms: 0.0 + -0.1 = -0.1 -2x + x2 = -0.1 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 = -0.1 + 1 Reorder the terms: 1 + -2x + x2 = -0.1 + 1 Combine like terms: -0.1 + 1 = 0.9 1 + -2x + x2 = 0.9 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.9 Calculate the square root of the right side: 0.948683298 Break this problem into two subproblems by setting (x + -1) equal to 0.948683298 and -0.948683298.Subproblem 1
x + -1 = 0.948683298 Simplifying x + -1 = 0.948683298 Reorder the terms: -1 + x = 0.948683298 Solving -1 + x = 0.948683298 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 = 0.948683298 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.948683298 + 1 x = 0.948683298 + 1 Combine like terms: 0.948683298 + 1 = 1.948683298 x = 1.948683298 Simplifying x = 1.948683298Subproblem 2
x + -1 = -0.948683298 Simplifying x + -1 = -0.948683298 Reorder the terms: -1 + x = -0.948683298 Solving -1 + x = -0.948683298 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 = -0.948683298 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.948683298 + 1 x = -0.948683298 + 1 Combine like terms: -0.948683298 + 1 = 0.051316702 x = 0.051316702 Simplifying x = 0.051316702Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.948683298, 0.051316702}
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