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Simplifying 0.03x2 + -1.2x + 8 = 0 Reorder the terms: 8 + -1.2x + 0.03x2 = 0 Solving 8 + -1.2x + 0.03x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. 266.6666667 + -40x + x2 = 0 Move the constant term to the right: Add '-266.6666667' to each side of the equation. 266.6666667 + -40x + -266.6666667 + x2 = 0 + -266.6666667 Reorder the terms: 266.6666667 + -266.6666667 + -40x + x2 = 0 + -266.6666667 Combine like terms: 266.6666667 + -266.6666667 = 0.0000000 0.0000000 + -40x + x2 = 0 + -266.6666667 -40x + x2 = 0 + -266.6666667 Combine like terms: 0 + -266.6666667 = -266.6666667 -40x + x2 = -266.6666667 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -266.6666667 + 400 Reorder the terms: 400 + -40x + x2 = -266.6666667 + 400 Combine like terms: -266.6666667 + 400 = 133.3333333 400 + -40x + x2 = 133.3333333 Factor a perfect square on the left side: (x + -20)(x + -20) = 133.3333333 Calculate the square root of the right side: 11.547005382 Break this problem into two subproblems by setting (x + -20) equal to 11.547005382 and -11.547005382.Subproblem 1
x + -20 = 11.547005382 Simplifying x + -20 = 11.547005382 Reorder the terms: -20 + x = 11.547005382 Solving -20 + x = 11.547005382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 11.547005382 + 20 Combine like terms: -20 + 20 = 0 0 + x = 11.547005382 + 20 x = 11.547005382 + 20 Combine like terms: 11.547005382 + 20 = 31.547005382 x = 31.547005382 Simplifying x = 31.547005382Subproblem 2
x + -20 = -11.547005382 Simplifying x + -20 = -11.547005382 Reorder the terms: -20 + x = -11.547005382 Solving -20 + x = -11.547005382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -11.547005382 + 20 Combine like terms: -20 + 20 = 0 0 + x = -11.547005382 + 20 x = -11.547005382 + 20 Combine like terms: -11.547005382 + 20 = 8.452994618 x = 8.452994618 Simplifying x = 8.452994618Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.547005382, 8.452994618}
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