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Simplifying x = 80 + -6 * 3x2 Multiply -6 * 3 x = 80 + -18x2 Solving x = 80 + -18x2 Solving for variable 'x'. Reorder the terms: -80 + x + 18x2 = 80 + -18x2 + -80 + 18x2 Reorder the terms: -80 + x + 18x2 = 80 + -80 + -18x2 + 18x2 Combine like terms: 80 + -80 = 0 -80 + x + 18x2 = 0 + -18x2 + 18x2 -80 + x + 18x2 = -18x2 + 18x2 Combine like terms: -18x2 + 18x2 = 0 -80 + x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -4.444444444 + 0.05555555556x + x2 = 0 Move the constant term to the right: Add '4.444444444' to each side of the equation. -4.444444444 + 0.05555555556x + 4.444444444 + x2 = 0 + 4.444444444 Reorder the terms: -4.444444444 + 4.444444444 + 0.05555555556x + x2 = 0 + 4.444444444 Combine like terms: -4.444444444 + 4.444444444 = 0.000000000 0.000000000 + 0.05555555556x + x2 = 0 + 4.444444444 0.05555555556x + x2 = 0 + 4.444444444 Combine like terms: 0 + 4.444444444 = 4.444444444 0.05555555556x + x2 = 4.444444444 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.05555555556x + 0.25 + x2 = 4.444444444 + 0.25 Reorder the terms: 0.25 + 0.05555555556x + x2 = 4.444444444 + 0.25 Combine like terms: 4.444444444 + 0.25 = 4.694444444 0.25 + 0.05555555556x + x2 = 4.694444444 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.694444444 Calculate the square root of the right side: 2.166666667 Break this problem into two subproblems by setting (x + 0.5) equal to 2.166666667 and -2.166666667.Subproblem 1
x + 0.5 = 2.166666667 Simplifying x + 0.5 = 2.166666667 Reorder the terms: 0.5 + x = 2.166666667 Solving 0.5 + x = 2.166666667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.166666667 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.166666667 + -0.5 x = 2.166666667 + -0.5 Combine like terms: 2.166666667 + -0.5 = 1.666666667 x = 1.666666667 Simplifying x = 1.666666667Subproblem 2
x + 0.5 = -2.166666667 Simplifying x + 0.5 = -2.166666667 Reorder the terms: 0.5 + x = -2.166666667 Solving 0.5 + x = -2.166666667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.166666667 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.166666667 + -0.5 x = -2.166666667 + -0.5 Combine like terms: -2.166666667 + -0.5 = -2.666666667 x = -2.666666667 Simplifying x = -2.666666667Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.666666667, -2.666666667}
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