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Simplifying 0.64x2 + -9x + -7000 = 0 Reorder the terms: -7000 + -9x + 0.64x2 = 0 Solving -7000 + -9x + 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 + -14.0625x + x2 = 0 Move the constant term to the right: Add '10937.5' to each side of the equation. -10937.5 + -14.0625x + 10937.5 + x2 = 0 + 10937.5 Reorder the terms: -10937.5 + 10937.5 + -14.0625x + x2 = 0 + 10937.5 Combine like terms: -10937.5 + 10937.5 = 0.0 0.0 + -14.0625x + x2 = 0 + 10937.5 -14.0625x + x2 = 0 + 10937.5 Combine like terms: 0 + 10937.5 = 10937.5 -14.0625x + x2 = 10937.5 The x term is -14.0625x. Take half its coefficient (-7.03125). Square it (49.43847656) and add it to both sides. Add '49.43847656' to each side of the equation. -14.0625x + 49.43847656 + x2 = 10937.5 + 49.43847656 Reorder the terms: 49.43847656 + -14.0625x + x2 = 10937.5 + 49.43847656 Combine like terms: 10937.5 + 49.43847656 = 10986.93847656 49.43847656 + -14.0625x + x2 = 10986.93847656 Factor a perfect square on the left side: (x + -7.03125)(x + -7.03125) = 10986.93847656 Calculate the square root of the right side: 104.818597952 Break this problem into two subproblems by setting (x + -7.03125) equal to 104.818597952 and -104.818597952.Subproblem 1
x + -7.03125 = 104.818597952 Simplifying x + -7.03125 = 104.818597952 Reorder the terms: -7.03125 + x = 104.818597952 Solving -7.03125 + x = 104.818597952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.03125' to each side of the equation. -7.03125 + 7.03125 + x = 104.818597952 + 7.03125 Combine like terms: -7.03125 + 7.03125 = 0.00000 0.00000 + x = 104.818597952 + 7.03125 x = 104.818597952 + 7.03125 Combine like terms: 104.818597952 + 7.03125 = 111.849847952 x = 111.849847952 Simplifying x = 111.849847952Subproblem 2
x + -7.03125 = -104.818597952 Simplifying x + -7.03125 = -104.818597952 Reorder the terms: -7.03125 + x = -104.818597952 Solving -7.03125 + x = -104.818597952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.03125' to each side of the equation. -7.03125 + 7.03125 + x = -104.818597952 + 7.03125 Combine like terms: -7.03125 + 7.03125 = 0.00000 0.00000 + x = -104.818597952 + 7.03125 x = -104.818597952 + 7.03125 Combine like terms: -104.818597952 + 7.03125 = -97.787347952 x = -97.787347952 Simplifying x = -97.787347952Solution
The solution to the problem is based on the solutions from the subproblems. x = {111.849847952, -97.787347952}
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