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Simplifying x2 + 0.04x + -1.47 = 0 Reorder the terms: -1.47 + 0.04x + x2 = 0 Solving -1.47 + 0.04x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.47' to each side of the equation. -1.47 + 0.04x + 1.47 + x2 = 0 + 1.47 Reorder the terms: -1.47 + 1.47 + 0.04x + x2 = 0 + 1.47 Combine like terms: -1.47 + 1.47 = 0.00 0.00 + 0.04x + x2 = 0 + 1.47 0.04x + x2 = 0 + 1.47 Combine like terms: 0 + 1.47 = 1.47 0.04x + x2 = 1.47 The x term is 0.04x. Take half its coefficient (0.02). Square it (0.0004) and add it to both sides. Add '0.0004' to each side of the equation. 0.04x + 0.0004 + x2 = 1.47 + 0.0004 Reorder the terms: 0.0004 + 0.04x + x2 = 1.47 + 0.0004 Combine like terms: 1.47 + 0.0004 = 1.4704 0.0004 + 0.04x + x2 = 1.4704 Factor a perfect square on the left side: (x + 0.02)(x + 0.02) = 1.4704 Calculate the square root of the right side: 1.212600511 Break this problem into two subproblems by setting (x + 0.02) equal to 1.212600511 and -1.212600511.Subproblem 1
x + 0.02 = 1.212600511 Simplifying x + 0.02 = 1.212600511 Reorder the terms: 0.02 + x = 1.212600511 Solving 0.02 + x = 1.212600511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02' to each side of the equation. 0.02 + -0.02 + x = 1.212600511 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + x = 1.212600511 + -0.02 x = 1.212600511 + -0.02 Combine like terms: 1.212600511 + -0.02 = 1.192600511 x = 1.192600511 Simplifying x = 1.192600511Subproblem 2
x + 0.02 = -1.212600511 Simplifying x + 0.02 = -1.212600511 Reorder the terms: 0.02 + x = -1.212600511 Solving 0.02 + x = -1.212600511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02' to each side of the equation. 0.02 + -0.02 + x = -1.212600511 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + x = -1.212600511 + -0.02 x = -1.212600511 + -0.02 Combine like terms: -1.212600511 + -0.02 = -1.232600511 x = -1.232600511 Simplifying x = -1.232600511Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.192600511, -1.232600511}
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