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Simplifying 12x + -1x2 = 12.8 Solving 12x + -1x2 = 12.8 Solving for variable 'x'. Reorder the terms: -12.8 + 12x + -1x2 = 12.8 + -12.8 Combine like terms: 12.8 + -12.8 = 0.0 -12.8 + 12x + -1x2 = 0.0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12.8 + -12x + x2 = 0.0 Move the constant term to the right: Add '-12.8' to each side of the equation. 12.8 + -12x + -12.8 + x2 = 0.0 + -12.8 Reorder the terms: 12.8 + -12.8 + -12x + x2 = 0.0 + -12.8 Combine like terms: 12.8 + -12.8 = 0.0 0.0 + -12x + x2 = 0.0 + -12.8 -12x + x2 = 0.0 + -12.8 Combine like terms: 0.0 + -12.8 = -12.8 -12x + x2 = -12.8 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -12.8 + 36 Reorder the terms: 36 + -12x + x2 = -12.8 + 36 Combine like terms: -12.8 + 36 = 23.2 36 + -12x + x2 = 23.2 Factor a perfect square on the left side: (x + -6)(x + -6) = 23.2 Calculate the square root of the right side: 4.816637832 Break this problem into two subproblems by setting (x + -6) equal to 4.816637832 and -4.816637832.Subproblem 1
x + -6 = 4.816637832 Simplifying x + -6 = 4.816637832 Reorder the terms: -6 + x = 4.816637832 Solving -6 + x = 4.816637832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 4.816637832 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.816637832 + 6 x = 4.816637832 + 6 Combine like terms: 4.816637832 + 6 = 10.816637832 x = 10.816637832 Simplifying x = 10.816637832Subproblem 2
x + -6 = -4.816637832 Simplifying x + -6 = -4.816637832 Reorder the terms: -6 + x = -4.816637832 Solving -6 + x = -4.816637832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -4.816637832 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.816637832 + 6 x = -4.816637832 + 6 Combine like terms: -4.816637832 + 6 = 1.183362168 x = 1.183362168 Simplifying x = 1.183362168Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.816637832, 1.183362168}
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