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Simplifying 0 = 0.03x2 + -1.2x + 2 Reorder the terms: 0 = 2 + -1.2x + 0.03x2 Solving 0 = 2 + -1.2x + 0.03x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + 1.2x + -0.03x2 = 2 + -1.2x + 0.03x2 + -2 + 1.2x + -0.03x2 Reorder the terms: -2 + 1.2x + -0.03x2 = 2 + -2 + -1.2x + 1.2x + 0.03x2 + -0.03x2 Combine like terms: 2 + -2 = 0 -2 + 1.2x + -0.03x2 = 0 + -1.2x + 1.2x + 0.03x2 + -0.03x2 -2 + 1.2x + -0.03x2 = -1.2x + 1.2x + 0.03x2 + -0.03x2 Combine like terms: -1.2x + 1.2x = 0.0 -2 + 1.2x + -0.03x2 = 0.0 + 0.03x2 + -0.03x2 -2 + 1.2x + -0.03x2 = 0.03x2 + -0.03x2 Combine like terms: 0.03x2 + -0.03x2 = 0.00 -2 + 1.2x + -0.03x2 = 0.00 Begin completing the square. Divide all terms by -0.03 the coefficient of the squared term: Divide each side by '-0.03'. 66.66666667 + -40x + x2 = 0 Move the constant term to the right: Add '-66.66666667' to each side of the equation. 66.66666667 + -40x + -66.66666667 + x2 = 0 + -66.66666667 Reorder the terms: 66.66666667 + -66.66666667 + -40x + x2 = 0 + -66.66666667 Combine like terms: 66.66666667 + -66.66666667 = 0.00000000 0.00000000 + -40x + x2 = 0 + -66.66666667 -40x + x2 = 0 + -66.66666667 Combine like terms: 0 + -66.66666667 = -66.66666667 -40x + x2 = -66.66666667 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 = -66.66666667 + 400 Reorder the terms: 400 + -40x + x2 = -66.66666667 + 400 Combine like terms: -66.66666667 + 400 = 333.33333333 400 + -40x + x2 = 333.33333333 Factor a perfect square on the left side: (x + -20)(x + -20) = 333.33333333 Calculate the square root of the right side: 18.257418583 Break this problem into two subproblems by setting (x + -20) equal to 18.257418583 and -18.257418583.Subproblem 1
x + -20 = 18.257418583 Simplifying x + -20 = 18.257418583 Reorder the terms: -20 + x = 18.257418583 Solving -20 + x = 18.257418583 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 = 18.257418583 + 20 Combine like terms: -20 + 20 = 0 0 + x = 18.257418583 + 20 x = 18.257418583 + 20 Combine like terms: 18.257418583 + 20 = 38.257418583 x = 38.257418583 Simplifying x = 38.257418583Subproblem 2
x + -20 = -18.257418583 Simplifying x + -20 = -18.257418583 Reorder the terms: -20 + x = -18.257418583 Solving -20 + x = -18.257418583 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 = -18.257418583 + 20 Combine like terms: -20 + 20 = 0 0 + x = -18.257418583 + 20 x = -18.257418583 + 20 Combine like terms: -18.257418583 + 20 = 1.742581417 x = 1.742581417 Simplifying x = 1.742581417Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.257418583, 1.742581417}
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