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Simplifying 0.7x2 = 104x + 0.7 Reorder the terms: 0.7x2 = 0.7 + 104x Solving 0.7x2 = 0.7 + 104x Solving for variable 'x'. Reorder the terms: -0.7 + -104x + 0.7x2 = 0.7 + 104x + -0.7 + -104x Reorder the terms: -0.7 + -104x + 0.7x2 = 0.7 + -0.7 + 104x + -104x Combine like terms: 0.7 + -0.7 = 0.0 -0.7 + -104x + 0.7x2 = 0.0 + 104x + -104x -0.7 + -104x + 0.7x2 = 104x + -104x Combine like terms: 104x + -104x = 0 -0.7 + -104x + 0.7x2 = 0 Begin completing the square. Divide all terms by 0.7 the coefficient of the squared term: Divide each side by '0.7'. -1 + -148.5714286x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -148.5714286x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -148.5714286x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -148.5714286x + x2 = 0 + 1 -148.5714286x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -148.5714286x + x2 = 1 The x term is -148.5714286x. Take half its coefficient (-74.2857143). Square it (5518.367349) and add it to both sides. Add '5518.367349' to each side of the equation. -148.5714286x + 5518.367349 + x2 = 1 + 5518.367349 Reorder the terms: 5518.367349 + -148.5714286x + x2 = 1 + 5518.367349 Combine like terms: 1 + 5518.367349 = 5519.367349 5518.367349 + -148.5714286x + x2 = 5519.367349 Factor a perfect square on the left side: (x + -74.2857143)(x + -74.2857143) = 5519.367349 Calculate the square root of the right side: 74.292444764 Break this problem into two subproblems by setting (x + -74.2857143) equal to 74.292444764 and -74.292444764.Subproblem 1
x + -74.2857143 = 74.292444764 Simplifying x + -74.2857143 = 74.292444764 Reorder the terms: -74.2857143 + x = 74.292444764 Solving -74.2857143 + x = 74.292444764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '74.2857143' to each side of the equation. -74.2857143 + 74.2857143 + x = 74.292444764 + 74.2857143 Combine like terms: -74.2857143 + 74.2857143 = 0.0000000 0.0000000 + x = 74.292444764 + 74.2857143 x = 74.292444764 + 74.2857143 Combine like terms: 74.292444764 + 74.2857143 = 148.578159064 x = 148.578159064 Simplifying x = 148.578159064Subproblem 2
x + -74.2857143 = -74.292444764 Simplifying x + -74.2857143 = -74.292444764 Reorder the terms: -74.2857143 + x = -74.292444764 Solving -74.2857143 + x = -74.292444764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '74.2857143' to each side of the equation. -74.2857143 + 74.2857143 + x = -74.292444764 + 74.2857143 Combine like terms: -74.2857143 + 74.2857143 = 0.0000000 0.0000000 + x = -74.292444764 + 74.2857143 x = -74.292444764 + 74.2857143 Combine like terms: -74.292444764 + 74.2857143 = -0.006730464 x = -0.006730464 Simplifying x = -0.006730464Solution
The solution to the problem is based on the solutions from the subproblems. x = {148.578159064, -0.006730464}
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