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Simplifying 2x2 + -4.6x + 1.2 = 0 Reorder the terms: 1.2 + -4.6x + 2x2 = 0 Solving 1.2 + -4.6x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.6 + -2.3x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -2.3x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -2.3x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -2.3x + x2 = 0 + -0.6 -2.3x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -2.3x + x2 = -0.6 The x term is -2.3x. Take half its coefficient (-1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. -2.3x + 1.3225 + x2 = -0.6 + 1.3225 Reorder the terms: 1.3225 + -2.3x + x2 = -0.6 + 1.3225 Combine like terms: -0.6 + 1.3225 = 0.7225 1.3225 + -2.3x + x2 = 0.7225 Factor a perfect square on the left side: (x + -1.15)(x + -1.15) = 0.7225 Calculate the square root of the right side: 0.85 Break this problem into two subproblems by setting (x + -1.15) equal to 0.85 and -0.85.Subproblem 1
x + -1.15 = 0.85 Simplifying x + -1.15 = 0.85 Reorder the terms: -1.15 + x = 0.85 Solving -1.15 + x = 0.85 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = 0.85 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = 0.85 + 1.15 x = 0.85 + 1.15 Combine like terms: 0.85 + 1.15 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -1.15 = -0.85 Simplifying x + -1.15 = -0.85 Reorder the terms: -1.15 + x = -0.85 Solving -1.15 + x = -0.85 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = -0.85 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = -0.85 + 1.15 x = -0.85 + 1.15 Combine like terms: -0.85 + 1.15 = 0.3 x = 0.3 Simplifying x = 0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, 0.3}
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