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Simplifying 6x2 + -195x + 1000 = 0 Reorder the terms: 1000 + -195x + 6x2 = 0 Solving 1000 + -195x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 166.6666667 + -32.5x + x2 = 0 Move the constant term to the right: Add '-166.6666667' to each side of the equation. 166.6666667 + -32.5x + -166.6666667 + x2 = 0 + -166.6666667 Reorder the terms: 166.6666667 + -166.6666667 + -32.5x + x2 = 0 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + -32.5x + x2 = 0 + -166.6666667 -32.5x + x2 = 0 + -166.6666667 Combine like terms: 0 + -166.6666667 = -166.6666667 -32.5x + x2 = -166.6666667 The x term is -32.5x. Take half its coefficient (-16.25). Square it (264.0625) and add it to both sides. Add '264.0625' to each side of the equation. -32.5x + 264.0625 + x2 = -166.6666667 + 264.0625 Reorder the terms: 264.0625 + -32.5x + x2 = -166.6666667 + 264.0625 Combine like terms: -166.6666667 + 264.0625 = 97.3958333 264.0625 + -32.5x + x2 = 97.3958333 Factor a perfect square on the left side: (x + -16.25)(x + -16.25) = 97.3958333 Calculate the square root of the right side: 9.868932734 Break this problem into two subproblems by setting (x + -16.25) equal to 9.868932734 and -9.868932734.Subproblem 1
x + -16.25 = 9.868932734 Simplifying x + -16.25 = 9.868932734 Reorder the terms: -16.25 + x = 9.868932734 Solving -16.25 + x = 9.868932734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.25' to each side of the equation. -16.25 + 16.25 + x = 9.868932734 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + x = 9.868932734 + 16.25 x = 9.868932734 + 16.25 Combine like terms: 9.868932734 + 16.25 = 26.118932734 x = 26.118932734 Simplifying x = 26.118932734Subproblem 2
x + -16.25 = -9.868932734 Simplifying x + -16.25 = -9.868932734 Reorder the terms: -16.25 + x = -9.868932734 Solving -16.25 + x = -9.868932734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.25' to each side of the equation. -16.25 + 16.25 + x = -9.868932734 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + x = -9.868932734 + 16.25 x = -9.868932734 + 16.25 Combine like terms: -9.868932734 + 16.25 = 6.381067266 x = 6.381067266 Simplifying x = 6.381067266Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.118932734, 6.381067266}
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