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Simplifying 20x2 + -28x + 5 = 0 Reorder the terms: 5 + -28x + 20x2 = 0 Solving 5 + -28x + 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'. 0.25 + -1.4x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.4x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.4x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.4x + x2 = 0 + -0.25 -1.4x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.4x + x2 = -0.25 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = -0.25 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = -0.25 + 0.49 Combine like terms: -0.25 + 0.49 = 0.24 0.49 + -1.4x + x2 = 0.24 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x + -0.7) equal to 0.489897949 and -0.489897949.Subproblem 1
x + -0.7 = 0.489897949 Simplifying x + -0.7 = 0.489897949 Reorder the terms: -0.7 + x = 0.489897949 Solving -0.7 + x = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.489897949 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.489897949 + 0.7 x = 0.489897949 + 0.7 Combine like terms: 0.489897949 + 0.7 = 1.189897949 x = 1.189897949 Simplifying x = 1.189897949Subproblem 2
x + -0.7 = -0.489897949 Simplifying x + -0.7 = -0.489897949 Reorder the terms: -0.7 + x = -0.489897949 Solving -0.7 + x = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -0.489897949 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.489897949 + 0.7 x = -0.489897949 + 0.7 Combine like terms: -0.489897949 + 0.7 = 0.210102051 x = 0.210102051 Simplifying x = 0.210102051Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.189897949, 0.210102051}
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