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Simplifying 10x2 + 2.2x + -1 = 0 Reorder the terms: -1 + 2.2x + 10x2 = 0 Solving -1 + 2.2x + 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 + 0.22x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.22x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.22x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.22x + x2 = 0 + 0.1 0.22x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 0.22x + x2 = 0.1 The x term is 0.22x. Take half its coefficient (0.11). Square it (0.0121) and add it to both sides. Add '0.0121' to each side of the equation. 0.22x + 0.0121 + x2 = 0.1 + 0.0121 Reorder the terms: 0.0121 + 0.22x + x2 = 0.1 + 0.0121 Combine like terms: 0.1 + 0.0121 = 0.1121 0.0121 + 0.22x + x2 = 0.1121 Factor a perfect square on the left side: (x + 0.11)(x + 0.11) = 0.1121 Calculate the square root of the right side: 0.334813381 Break this problem into two subproblems by setting (x + 0.11) equal to 0.334813381 and -0.334813381.Subproblem 1
x + 0.11 = 0.334813381 Simplifying x + 0.11 = 0.334813381 Reorder the terms: 0.11 + x = 0.334813381 Solving 0.11 + x = 0.334813381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.11' to each side of the equation. 0.11 + -0.11 + x = 0.334813381 + -0.11 Combine like terms: 0.11 + -0.11 = 0.00 0.00 + x = 0.334813381 + -0.11 x = 0.334813381 + -0.11 Combine like terms: 0.334813381 + -0.11 = 0.224813381 x = 0.224813381 Simplifying x = 0.224813381Subproblem 2
x + 0.11 = -0.334813381 Simplifying x + 0.11 = -0.334813381 Reorder the terms: 0.11 + x = -0.334813381 Solving 0.11 + x = -0.334813381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.11' to each side of the equation. 0.11 + -0.11 + x = -0.334813381 + -0.11 Combine like terms: 0.11 + -0.11 = 0.00 0.00 + x = -0.334813381 + -0.11 x = -0.334813381 + -0.11 Combine like terms: -0.334813381 + -0.11 = -0.444813381 x = -0.444813381 Simplifying x = -0.444813381Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.224813381, -0.444813381}
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