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Simplifying x2 + -1.4x + 0.24 = 0 Reorder the terms: 0.24 + -1.4x + x2 = 0 Solving 0.24 + -1.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.24' to each side of the equation. 0.24 + -1.4x + -0.24 + x2 = 0 + -0.24 Reorder the terms: 0.24 + -0.24 + -1.4x + x2 = 0 + -0.24 Combine like terms: 0.24 + -0.24 = 0.00 0.00 + -1.4x + x2 = 0 + -0.24 -1.4x + x2 = 0 + -0.24 Combine like terms: 0 + -0.24 = -0.24 -1.4x + x2 = -0.24 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 = -0.24 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = -0.24 + 0.49 Combine like terms: -0.24 + 0.49 = 0.25 0.49 + -1.4x + x2 = 0.25 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + -0.7) equal to 0.5 and -0.5.Subproblem 1
x + -0.7 = 0.5 Simplifying x + -0.7 = 0.5 Reorder the terms: -0.7 + x = 0.5 Solving -0.7 + x = 0.5 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 = 0.5 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.5 + 0.7 x = 0.5 + 0.7 Combine like terms: 0.5 + 0.7 = 1.2 x = 1.2 Simplifying x = 1.2Subproblem 2
x + -0.7 = -0.5 Simplifying x + -0.7 = -0.5 Reorder the terms: -0.7 + x = -0.5 Solving -0.7 + x = -0.5 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 = -0.5 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.5 + 0.7 x = -0.5 + 0.7 Combine like terms: -0.5 + 0.7 = 0.2 x = 0.2 Simplifying x = 0.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2, 0.2}
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