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Simplifying 0.6x2 = 3.6x + 0.06 Reorder the terms: 0.6x2 = 0.06 + 3.6x Solving 0.6x2 = 0.06 + 3.6x Solving for variable 'x'. Reorder the terms: -0.06 + -3.6x + 0.6x2 = 0.06 + 3.6x + -0.06 + -3.6x Reorder the terms: -0.06 + -3.6x + 0.6x2 = 0.06 + -0.06 + 3.6x + -3.6x Combine like terms: 0.06 + -0.06 = 0.00 -0.06 + -3.6x + 0.6x2 = 0.00 + 3.6x + -3.6x -0.06 + -3.6x + 0.6x2 = 3.6x + -3.6x Combine like terms: 3.6x + -3.6x = 0.0 -0.06 + -3.6x + 0.6x2 = 0.0 Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -0.1 + -6x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -6x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -6x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -6x + x2 = 0 + 0.1 -6x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -6x + x2 = 0.1 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 0.1 + 9 Reorder the terms: 9 + -6x + x2 = 0.1 + 9 Combine like terms: 0.1 + 9 = 9.1 9 + -6x + x2 = 9.1 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.1 Calculate the square root of the right side: 3.016620626 Break this problem into two subproblems by setting (x + -3) equal to 3.016620626 and -3.016620626.Subproblem 1
x + -3 = 3.016620626 Simplifying x + -3 = 3.016620626 Reorder the terms: -3 + x = 3.016620626 Solving -3 + x = 3.016620626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.016620626 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.016620626 + 3 x = 3.016620626 + 3 Combine like terms: 3.016620626 + 3 = 6.016620626 x = 6.016620626 Simplifying x = 6.016620626Subproblem 2
x + -3 = -3.016620626 Simplifying x + -3 = -3.016620626 Reorder the terms: -3 + x = -3.016620626 Solving -3 + x = -3.016620626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.016620626 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.016620626 + 3 x = -3.016620626 + 3 Combine like terms: -3.016620626 + 3 = -0.016620626 x = -0.016620626 Simplifying x = -0.016620626Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.016620626, -0.016620626}
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