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Simplifying -0.006x2 + 1.2x + 10 = 0 Reorder the terms: 10 + 1.2x + -0.006x2 = 0 Solving 10 + 1.2x + -0.006x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.006 the coefficient of the squared term: Divide each side by '-0.006'. -1666.666667 + -200x + x2 = 0 Move the constant term to the right: Add '1666.666667' to each side of the equation. -1666.666667 + -200x + 1666.666667 + x2 = 0 + 1666.666667 Reorder the terms: -1666.666667 + 1666.666667 + -200x + x2 = 0 + 1666.666667 Combine like terms: -1666.666667 + 1666.666667 = 0.000000 0.000000 + -200x + x2 = 0 + 1666.666667 -200x + x2 = 0 + 1666.666667 Combine like terms: 0 + 1666.666667 = 1666.666667 -200x + x2 = 1666.666667 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = 1666.666667 + 10000 Reorder the terms: 10000 + -200x + x2 = 1666.666667 + 10000 Combine like terms: 1666.666667 + 10000 = 11666.666667 10000 + -200x + x2 = 11666.666667 Factor a perfect square on the left side: (x + -100)(x + -100) = 11666.666667 Calculate the square root of the right side: 108.012344975 Break this problem into two subproblems by setting (x + -100) equal to 108.012344975 and -108.012344975.Subproblem 1
x + -100 = 108.012344975 Simplifying x + -100 = 108.012344975 Reorder the terms: -100 + x = 108.012344975 Solving -100 + x = 108.012344975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 108.012344975 + 100 Combine like terms: -100 + 100 = 0 0 + x = 108.012344975 + 100 x = 108.012344975 + 100 Combine like terms: 108.012344975 + 100 = 208.012344975 x = 208.012344975 Simplifying x = 208.012344975Subproblem 2
x + -100 = -108.012344975 Simplifying x + -100 = -108.012344975 Reorder the terms: -100 + x = -108.012344975 Solving -100 + x = -108.012344975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -108.012344975 + 100 Combine like terms: -100 + 100 = 0 0 + x = -108.012344975 + 100 x = -108.012344975 + 100 Combine like terms: -108.012344975 + 100 = -8.012344975 x = -8.012344975 Simplifying x = -8.012344975Solution
The solution to the problem is based on the solutions from the subproblems. x = {208.012344975, -8.012344975}
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