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Simplifying 0.2x2 + -6x + 60 = 250 Reorder the terms: 60 + -6x + 0.2x2 = 250 Solving 60 + -6x + 0.2x2 = 250 Solving for variable 'x'. Reorder the terms: 60 + -250 + -6x + 0.2x2 = 250 + -250 Combine like terms: 60 + -250 = -190 -190 + -6x + 0.2x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -190 + -6x + 0.2x2 = 0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -950 + -30x + x2 = 0 Move the constant term to the right: Add '950' to each side of the equation. -950 + -30x + 950 + x2 = 0 + 950 Reorder the terms: -950 + 950 + -30x + x2 = 0 + 950 Combine like terms: -950 + 950 = 0 0 + -30x + x2 = 0 + 950 -30x + x2 = 0 + 950 Combine like terms: 0 + 950 = 950 -30x + x2 = 950 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 950 + 225 Reorder the terms: 225 + -30x + x2 = 950 + 225 Combine like terms: 950 + 225 = 1175 225 + -30x + x2 = 1175 Factor a perfect square on the left side: (x + -15)(x + -15) = 1175 Calculate the square root of the right side: 34.278273002 Break this problem into two subproblems by setting (x + -15) equal to 34.278273002 and -34.278273002.Subproblem 1
x + -15 = 34.278273002 Simplifying x + -15 = 34.278273002 Reorder the terms: -15 + x = 34.278273002 Solving -15 + x = 34.278273002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 34.278273002 + 15 Combine like terms: -15 + 15 = 0 0 + x = 34.278273002 + 15 x = 34.278273002 + 15 Combine like terms: 34.278273002 + 15 = 49.278273002 x = 49.278273002 Simplifying x = 49.278273002Subproblem 2
x + -15 = -34.278273002 Simplifying x + -15 = -34.278273002 Reorder the terms: -15 + x = -34.278273002 Solving -15 + x = -34.278273002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -34.278273002 + 15 Combine like terms: -15 + 15 = 0 0 + x = -34.278273002 + 15 x = -34.278273002 + 15 Combine like terms: -34.278273002 + 15 = -19.278273002 x = -19.278273002 Simplifying x = -19.278273002Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.278273002, -19.278273002}
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