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Simplifying 0 = x2 + -2.4x + 0.8 Reorder the terms: 0 = 0.8 + -2.4x + x2 Solving 0 = 0.8 + -2.4x + x2 Solving for variable 'x'. Combine like terms: 0 + -0.8 = -0.8 -0.8 + 2.4x + -1x2 = 0.8 + -2.4x + x2 + -0.8 + 2.4x + -1x2 Reorder the terms: -0.8 + 2.4x + -1x2 = 0.8 + -0.8 + -2.4x + 2.4x + x2 + -1x2 Combine like terms: 0.8 + -0.8 = 0.0 -0.8 + 2.4x + -1x2 = 0.0 + -2.4x + 2.4x + x2 + -1x2 -0.8 + 2.4x + -1x2 = -2.4x + 2.4x + x2 + -1x2 Combine like terms: -2.4x + 2.4x = 0.0 -0.8 + 2.4x + -1x2 = 0.0 + x2 + -1x2 -0.8 + 2.4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -0.8 + 2.4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.8 + -2.4x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -2.4x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -2.4x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -2.4x + x2 = 0 + -0.8 -2.4x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -2.4x + x2 = -0.8 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -0.8 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -0.8 + 1.44 Combine like terms: -0.8 + 1.44 = 0.64 1.44 + -2.4x + x2 = 0.64 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 0.64 Calculate the square root of the right side: 0.8 Break this problem into two subproblems by setting (x + -1.2) equal to 0.8 and -0.8.Subproblem 1
x + -1.2 = 0.8 Simplifying x + -1.2 = 0.8 Reorder the terms: -1.2 + x = 0.8 Solving -1.2 + x = 0.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 0.8 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 0.8 + 1.2 x = 0.8 + 1.2 Combine like terms: 0.8 + 1.2 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -1.2 = -0.8 Simplifying x + -1.2 = -0.8 Reorder the terms: -1.2 + x = -0.8 Solving -1.2 + x = -0.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -0.8 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -0.8 + 1.2 x = -0.8 + 1.2 Combine like terms: -0.8 + 1.2 = 0.4 x = 0.4 Simplifying x = 0.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, 0.4}
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