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Simplifying -0.03x2 + 1.2x + 10 = 0 Reorder the terms: 10 + 1.2x + -0.03x2 = 0 Solving 10 + 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'. -333.3333333 + -40x + x2 = 0 Move the constant term to the right: Add '333.3333333' to each side of the equation. -333.3333333 + -40x + 333.3333333 + x2 = 0 + 333.3333333 Reorder the terms: -333.3333333 + 333.3333333 + -40x + x2 = 0 + 333.3333333 Combine like terms: -333.3333333 + 333.3333333 = 0.0000000 0.0000000 + -40x + x2 = 0 + 333.3333333 -40x + x2 = 0 + 333.3333333 Combine like terms: 0 + 333.3333333 = 333.3333333 -40x + x2 = 333.3333333 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 = 333.3333333 + 400 Reorder the terms: 400 + -40x + x2 = 333.3333333 + 400 Combine like terms: 333.3333333 + 400 = 733.3333333 400 + -40x + x2 = 733.3333333 Factor a perfect square on the left side: (x + -20)(x + -20) = 733.3333333 Calculate the square root of the right side: 27.080128015 Break this problem into two subproblems by setting (x + -20) equal to 27.080128015 and -27.080128015.Subproblem 1
x + -20 = 27.080128015 Simplifying x + -20 = 27.080128015 Reorder the terms: -20 + x = 27.080128015 Solving -20 + x = 27.080128015 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 = 27.080128015 + 20 Combine like terms: -20 + 20 = 0 0 + x = 27.080128015 + 20 x = 27.080128015 + 20 Combine like terms: 27.080128015 + 20 = 47.080128015 x = 47.080128015 Simplifying x = 47.080128015Subproblem 2
x + -20 = -27.080128015 Simplifying x + -20 = -27.080128015 Reorder the terms: -20 + x = -27.080128015 Solving -20 + x = -27.080128015 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 = -27.080128015 + 20 Combine like terms: -20 + 20 = 0 0 + x = -27.080128015 + 20 x = -27.080128015 + 20 Combine like terms: -27.080128015 + 20 = -7.080128015 x = -7.080128015 Simplifying x = -7.080128015Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.080128015, -7.080128015}
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