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Simplifying 10x2 + -22x + 5 = 0 Reorder the terms: 5 + -22x + 10x2 = 0 Solving 5 + -22x + 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'. 0.5 + -2.2x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -2.2x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -2.2x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -2.2x + x2 = 0 + -0.5 -2.2x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -2.2x + x2 = -0.5 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = -0.5 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = -0.5 + 1.21 Combine like terms: -0.5 + 1.21 = 0.71 1.21 + -2.2x + x2 = 0.71 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 0.71 Calculate the square root of the right side: 0.842614977 Break this problem into two subproblems by setting (x + -1.1) equal to 0.842614977 and -0.842614977.Subproblem 1
x + -1.1 = 0.842614977 Simplifying x + -1.1 = 0.842614977 Reorder the terms: -1.1 + x = 0.842614977 Solving -1.1 + x = 0.842614977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 0.842614977 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 0.842614977 + 1.1 x = 0.842614977 + 1.1 Combine like terms: 0.842614977 + 1.1 = 1.942614977 x = 1.942614977 Simplifying x = 1.942614977Subproblem 2
x + -1.1 = -0.842614977 Simplifying x + -1.1 = -0.842614977 Reorder the terms: -1.1 + x = -0.842614977 Solving -1.1 + x = -0.842614977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -0.842614977 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -0.842614977 + 1.1 x = -0.842614977 + 1.1 Combine like terms: -0.842614977 + 1.1 = 0.257385023 x = 0.257385023 Simplifying x = 0.257385023Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.942614977, 0.257385023}
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