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Simplifying -0.2x2 + 26x + 720 = 1000 Reorder the terms: 720 + 26x + -0.2x2 = 1000 Solving 720 + 26x + -0.2x2 = 1000 Solving for variable 'x'. Reorder the terms: 720 + -1000 + 26x + -0.2x2 = 1000 + -1000 Combine like terms: 720 + -1000 = -280 -280 + 26x + -0.2x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -280 + 26x + -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'. 1400 + -130x + x2 = 0 Move the constant term to the right: Add '-1400' to each side of the equation. 1400 + -130x + -1400 + x2 = 0 + -1400 Reorder the terms: 1400 + -1400 + -130x + x2 = 0 + -1400 Combine like terms: 1400 + -1400 = 0 0 + -130x + x2 = 0 + -1400 -130x + x2 = 0 + -1400 Combine like terms: 0 + -1400 = -1400 -130x + x2 = -1400 The x term is -130x. Take half its coefficient (-65). Square it (4225) and add it to both sides. Add '4225' to each side of the equation. -130x + 4225 + x2 = -1400 + 4225 Reorder the terms: 4225 + -130x + x2 = -1400 + 4225 Combine like terms: -1400 + 4225 = 2825 4225 + -130x + x2 = 2825 Factor a perfect square on the left side: (x + -65)(x + -65) = 2825 Calculate the square root of the right side: 53.150729064 Break this problem into two subproblems by setting (x + -65) equal to 53.150729064 and -53.150729064.Subproblem 1
x + -65 = 53.150729064 Simplifying x + -65 = 53.150729064 Reorder the terms: -65 + x = 53.150729064 Solving -65 + x = 53.150729064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = 53.150729064 + 65 Combine like terms: -65 + 65 = 0 0 + x = 53.150729064 + 65 x = 53.150729064 + 65 Combine like terms: 53.150729064 + 65 = 118.150729064 x = 118.150729064 Simplifying x = 118.150729064Subproblem 2
x + -65 = -53.150729064 Simplifying x + -65 = -53.150729064 Reorder the terms: -65 + x = -53.150729064 Solving -65 + x = -53.150729064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = -53.150729064 + 65 Combine like terms: -65 + 65 = 0 0 + x = -53.150729064 + 65 x = -53.150729064 + 65 Combine like terms: -53.150729064 + 65 = 11.849270936 x = 11.849270936 Simplifying x = 11.849270936Solution
The solution to the problem is based on the solutions from the subproblems. x = {118.150729064, 11.849270936}
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