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Simplifying 60 = 0.1x2 + 0.6x + 10 Reorder the terms: 60 = 10 + 0.6x + 0.1x2 Solving 60 = 10 + 0.6x + 0.1x2 Solving for variable 'x'. Combine like terms: 60 + -10 = 50 50 + -0.6x + -0.1x2 = 10 + 0.6x + 0.1x2 + -10 + -0.6x + -0.1x2 Reorder the terms: 50 + -0.6x + -0.1x2 = 10 + -10 + 0.6x + -0.6x + 0.1x2 + -0.1x2 Combine like terms: 10 + -10 = 0 50 + -0.6x + -0.1x2 = 0 + 0.6x + -0.6x + 0.1x2 + -0.1x2 50 + -0.6x + -0.1x2 = 0.6x + -0.6x + 0.1x2 + -0.1x2 Combine like terms: 0.6x + -0.6x = 0.0 50 + -0.6x + -0.1x2 = 0.0 + 0.1x2 + -0.1x2 50 + -0.6x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 50 + -0.6x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -500 + 6x + x2 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + 6x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + 6x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 6x + x2 = 0 + 500 6x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 6x + x2 = 500 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 = 500 + 9 Reorder the terms: 9 + 6x + x2 = 500 + 9 Combine like terms: 500 + 9 = 509 9 + 6x + x2 = 509 Factor a perfect square on the left side: (x + 3)(x + 3) = 509 Calculate the square root of the right side: 22.561028345 Break this problem into two subproblems by setting (x + 3) equal to 22.561028345 and -22.561028345.Subproblem 1
x + 3 = 22.561028345 Simplifying x + 3 = 22.561028345 Reorder the terms: 3 + x = 22.561028345 Solving 3 + x = 22.561028345 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 = 22.561028345 + -3 Combine like terms: 3 + -3 = 0 0 + x = 22.561028345 + -3 x = 22.561028345 + -3 Combine like terms: 22.561028345 + -3 = 19.561028345 x = 19.561028345 Simplifying x = 19.561028345Subproblem 2
x + 3 = -22.561028345 Simplifying x + 3 = -22.561028345 Reorder the terms: 3 + x = -22.561028345 Solving 3 + x = -22.561028345 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 = -22.561028345 + -3 Combine like terms: 3 + -3 = 0 0 + x = -22.561028345 + -3 x = -22.561028345 + -3 Combine like terms: -22.561028345 + -3 = -25.561028345 x = -25.561028345 Simplifying x = -25.561028345Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.561028345, -25.561028345}
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