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Simplifying -10x2 + -2x + 1 = 0 Reorder the terms: 1 + -2x + -10x2 = 0 Solving 1 + -2x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.1 + 0.2x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.2x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.2x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.2x + x2 = 0 + 0.1 0.2x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 0.2x + x2 = 0.1 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 0.1 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.1 + 0.01 Combine like terms: 0.1 + 0.01 = 0.11 0.01 + 0.2x + x2 = 0.11 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.11 Calculate the square root of the right side: 0.331662479 Break this problem into two subproblems by setting (x + 0.1) equal to 0.331662479 and -0.331662479.Subproblem 1
x + 0.1 = 0.331662479 Simplifying x + 0.1 = 0.331662479 Reorder the terms: 0.1 + x = 0.331662479 Solving 0.1 + x = 0.331662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.331662479 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.331662479 + -0.1 x = 0.331662479 + -0.1 Combine like terms: 0.331662479 + -0.1 = 0.231662479 x = 0.231662479 Simplifying x = 0.231662479Subproblem 2
x + 0.1 = -0.331662479 Simplifying x + 0.1 = -0.331662479 Reorder the terms: 0.1 + x = -0.331662479 Solving 0.1 + x = -0.331662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.331662479 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.331662479 + -0.1 x = -0.331662479 + -0.1 Combine like terms: -0.331662479 + -0.1 = -0.431662479 x = -0.431662479 Simplifying x = -0.431662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.231662479, -0.431662479}
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