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Simplifying 0.64x2 + -8x + -7000 = 0 Reorder the terms: -7000 + -8x + 0.64x2 = 0 Solving -7000 + -8x + 0.64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.64 the coefficient of the squared term: Divide each side by '0.64'. -10937.5 + -12.5x + x2 = 0 Move the constant term to the right: Add '10937.5' to each side of the equation. -10937.5 + -12.5x + 10937.5 + x2 = 0 + 10937.5 Reorder the terms: -10937.5 + 10937.5 + -12.5x + x2 = 0 + 10937.5 Combine like terms: -10937.5 + 10937.5 = 0.0 0.0 + -12.5x + x2 = 0 + 10937.5 -12.5x + x2 = 0 + 10937.5 Combine like terms: 0 + 10937.5 = 10937.5 -12.5x + x2 = 10937.5 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 10937.5 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 10937.5 + 39.0625 Combine like terms: 10937.5 + 39.0625 = 10976.5625 39.0625 + -12.5x + x2 = 10976.5625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 10976.5625 Calculate the square root of the right side: 104.769091339 Break this problem into two subproblems by setting (x + -6.25) equal to 104.769091339 and -104.769091339.Subproblem 1
x + -6.25 = 104.769091339 Simplifying x + -6.25 = 104.769091339 Reorder the terms: -6.25 + x = 104.769091339 Solving -6.25 + x = 104.769091339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 104.769091339 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 104.769091339 + 6.25 x = 104.769091339 + 6.25 Combine like terms: 104.769091339 + 6.25 = 111.019091339 x = 111.019091339 Simplifying x = 111.019091339Subproblem 2
x + -6.25 = -104.769091339 Simplifying x + -6.25 = -104.769091339 Reorder the terms: -6.25 + x = -104.769091339 Solving -6.25 + x = -104.769091339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -104.769091339 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -104.769091339 + 6.25 x = -104.769091339 + 6.25 Combine like terms: -104.769091339 + 6.25 = -98.519091339 x = -98.519091339 Simplifying x = -98.519091339Solution
The solution to the problem is based on the solutions from the subproblems. x = {111.019091339, -98.519091339}
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