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Simplifying 0.03x2 + 1.2x + -6 = 0 Reorder the terms: -6 + 1.2x + 0.03x2 = 0 Solving -6 + 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'. -200 + 40x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 40x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 40x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 40x + x2 = 0 + 200 40x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 40x + x2 = 200 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 = 200 + 400 Reorder the terms: 400 + 40x + x2 = 200 + 400 Combine like terms: 200 + 400 = 600 400 + 40x + x2 = 600 Factor a perfect square on the left side: (x + 20)(x + 20) = 600 Calculate the square root of the right side: 24.494897428 Break this problem into two subproblems by setting (x + 20) equal to 24.494897428 and -24.494897428.Subproblem 1
x + 20 = 24.494897428 Simplifying x + 20 = 24.494897428 Reorder the terms: 20 + x = 24.494897428 Solving 20 + x = 24.494897428 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 = 24.494897428 + -20 Combine like terms: 20 + -20 = 0 0 + x = 24.494897428 + -20 x = 24.494897428 + -20 Combine like terms: 24.494897428 + -20 = 4.494897428 x = 4.494897428 Simplifying x = 4.494897428Subproblem 2
x + 20 = -24.494897428 Simplifying x + 20 = -24.494897428 Reorder the terms: 20 + x = -24.494897428 Solving 20 + x = -24.494897428 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 = -24.494897428 + -20 Combine like terms: 20 + -20 = 0 0 + x = -24.494897428 + -20 x = -24.494897428 + -20 Combine like terms: -24.494897428 + -20 = -44.494897428 x = -44.494897428 Simplifying x = -44.494897428Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.494897428, -44.494897428}
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