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Simplifying -3x2 + 75x + 10 = 0 Reorder the terms: 10 + 75x + -3x2 = 0 Solving 10 + 75x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -3.333333333 + -25x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -25x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -25x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -25x + x2 = 0 + 3.333333333 -25x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -25x + x2 = 3.333333333 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = 3.333333333 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 3.333333333 + 156.25 Combine like terms: 3.333333333 + 156.25 = 159.583333333 156.25 + -25x + x2 = 159.583333333 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 159.583333333 Calculate the square root of the right side: 12.632629708 Break this problem into two subproblems by setting (x + -12.5) equal to 12.632629708 and -12.632629708.Subproblem 1
x + -12.5 = 12.632629708 Simplifying x + -12.5 = 12.632629708 Reorder the terms: -12.5 + x = 12.632629708 Solving -12.5 + x = 12.632629708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 12.632629708 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.632629708 + 12.5 x = 12.632629708 + 12.5 Combine like terms: 12.632629708 + 12.5 = 25.132629708 x = 25.132629708 Simplifying x = 25.132629708Subproblem 2
x + -12.5 = -12.632629708 Simplifying x + -12.5 = -12.632629708 Reorder the terms: -12.5 + x = -12.632629708 Solving -12.5 + x = -12.632629708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -12.632629708 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.632629708 + 12.5 x = -12.632629708 + 12.5 Combine like terms: -12.632629708 + 12.5 = -0.132629708 x = -0.132629708 Simplifying x = -0.132629708Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.132629708, -0.132629708}
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