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