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Simplifying x2 + 0.12x + -0.8 = 0 Reorder the terms: -0.8 + 0.12x + x2 = 0 Solving -0.8 + 0.12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.12x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.12x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.12x + x2 = 0 + 0.8 0.12x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.12x + x2 = 0.8 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 = 0.8 + 0.0036 Reorder the terms: 0.0036 + 0.12x + x2 = 0.8 + 0.0036 Combine like terms: 0.8 + 0.0036 = 0.8036 0.0036 + 0.12x + x2 = 0.8036 Factor a perfect square on the left side: (x + 0.06)(x + 0.06) = 0.8036 Calculate the square root of the right side: 0.896437393 Break this problem into two subproblems by setting (x + 0.06) equal to 0.896437393 and -0.896437393.Subproblem 1
x + 0.06 = 0.896437393 Simplifying x + 0.06 = 0.896437393 Reorder the terms: 0.06 + x = 0.896437393 Solving 0.06 + x = 0.896437393 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 = 0.896437393 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = 0.896437393 + -0.06 x = 0.896437393 + -0.06 Combine like terms: 0.896437393 + -0.06 = 0.836437393 x = 0.836437393 Simplifying x = 0.836437393Subproblem 2
x + 0.06 = -0.896437393 Simplifying x + 0.06 = -0.896437393 Reorder the terms: 0.06 + x = -0.896437393 Solving 0.06 + x = -0.896437393 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 = -0.896437393 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = -0.896437393 + -0.06 x = -0.896437393 + -0.06 Combine like terms: -0.896437393 + -0.06 = -0.956437393 x = -0.956437393 Simplifying x = -0.956437393Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.836437393, -0.956437393}
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