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Simplifying x2 + 0.12x + -1.2 = 0 Reorder the terms: -1.2 + 0.12x + x2 = 0 Solving -1.2 + 0.12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.12x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.12x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.12x + x2 = 0 + 1.2 0.12x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.12x + x2 = 1.2 The x term is 0.12x. Take half its coefficient (0.06). Square it (0.0036) and add it to both sides. Add '0.0036' to each side of the equation. 0.12x + 0.0036 + x2 = 1.2 + 0.0036 Reorder the terms: 0.0036 + 0.12x + x2 = 1.2 + 0.0036 Combine like terms: 1.2 + 0.0036 = 1.2036 0.0036 + 0.12x + x2 = 1.2036 Factor a perfect square on the left side: (x + 0.06)(x + 0.06) = 1.2036 Calculate the square root of the right side: 1.097087052 Break this problem into two subproblems by setting (x + 0.06) equal to 1.097087052 and -1.097087052.Subproblem 1
x + 0.06 = 1.097087052 Simplifying x + 0.06 = 1.097087052 Reorder the terms: 0.06 + x = 1.097087052 Solving 0.06 + x = 1.097087052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = 1.097087052 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = 1.097087052 + -0.06 x = 1.097087052 + -0.06 Combine like terms: 1.097087052 + -0.06 = 1.037087052 x = 1.037087052 Simplifying x = 1.037087052Subproblem 2
x + 0.06 = -1.097087052 Simplifying x + 0.06 = -1.097087052 Reorder the terms: 0.06 + x = -1.097087052 Solving 0.06 + x = -1.097087052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = -1.097087052 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = -1.097087052 + -0.06 x = -1.097087052 + -0.06 Combine like terms: -1.097087052 + -0.06 = -1.157087052 x = -1.157087052 Simplifying x = -1.157087052Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.037087052, -1.157087052}
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