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Simplifying x2 + 1.4x + 0.49 = 3 Reorder the terms: 0.49 + 1.4x + x2 = 3 Solving 0.49 + 1.4x + x2 = 3 Solving for variable 'x'. Reorder the terms: 0.49 + -3 + 1.4x + x2 = 3 + -3 Combine like terms: 0.49 + -3 = -2.51 -2.51 + 1.4x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -2.51 + 1.4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2.51' to each side of the equation. -2.51 + 1.4x + 2.51 + x2 = 0 + 2.51 Reorder the terms: -2.51 + 2.51 + 1.4x + x2 = 0 + 2.51 Combine like terms: -2.51 + 2.51 = 0.00 0.00 + 1.4x + x2 = 0 + 2.51 1.4x + x2 = 0 + 2.51 Combine like terms: 0 + 2.51 = 2.51 1.4x + x2 = 2.51 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 = 2.51 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 2.51 + 0.49 Combine like terms: 2.51 + 0.49 = 3 0.49 + 1.4x + x2 = 3 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 0.7) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 0.7 = 1.732050808 Simplifying x + 0.7 = 1.732050808 Reorder the terms: 0.7 + x = 1.732050808 Solving 0.7 + x = 1.732050808 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 = 1.732050808 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 1.732050808 + -0.7 x = 1.732050808 + -0.7 Combine like terms: 1.732050808 + -0.7 = 1.032050808 x = 1.032050808 Simplifying x = 1.032050808Subproblem 2
x + 0.7 = -1.732050808 Simplifying x + 0.7 = -1.732050808 Reorder the terms: 0.7 + x = -1.732050808 Solving 0.7 + x = -1.732050808 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 = -1.732050808 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -1.732050808 + -0.7 x = -1.732050808 + -0.7 Combine like terms: -1.732050808 + -0.7 = -2.432050808 x = -2.432050808 Simplifying x = -2.432050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.032050808, -2.432050808}
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