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Simplifying 20x2 + -44x + 23 = 0 Reorder the terms: 23 + -44x + 20x2 = 0 Solving 23 + -44x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 1.15 + -2.2x + x2 = 0 Move the constant term to the right: Add '-1.15' to each side of the equation. 1.15 + -2.2x + -1.15 + x2 = 0 + -1.15 Reorder the terms: 1.15 + -1.15 + -2.2x + x2 = 0 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + -2.2x + x2 = 0 + -1.15 -2.2x + x2 = 0 + -1.15 Combine like terms: 0 + -1.15 = -1.15 -2.2x + x2 = -1.15 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 = -1.15 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = -1.15 + 1.21 Combine like terms: -1.15 + 1.21 = 0.06 1.21 + -2.2x + x2 = 0.06 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 0.06 Calculate the square root of the right side: 0.244948974 Break this problem into two subproblems by setting (x + -1.1) equal to 0.244948974 and -0.244948974.Subproblem 1
x + -1.1 = 0.244948974 Simplifying x + -1.1 = 0.244948974 Reorder the terms: -1.1 + x = 0.244948974 Solving -1.1 + x = 0.244948974 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 = 0.244948974 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 0.244948974 + 1.1 x = 0.244948974 + 1.1 Combine like terms: 0.244948974 + 1.1 = 1.344948974 x = 1.344948974 Simplifying x = 1.344948974Subproblem 2
x + -1.1 = -0.244948974 Simplifying x + -1.1 = -0.244948974 Reorder the terms: -1.1 + x = -0.244948974 Solving -1.1 + x = -0.244948974 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 = -0.244948974 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -0.244948974 + 1.1 x = -0.244948974 + 1.1 Combine like terms: -0.244948974 + 1.1 = 0.855051026 x = 0.855051026 Simplifying x = 0.855051026Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.344948974, 0.855051026}
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