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Simplifying 0 = -0.275x2 + 6.05x + 250 Reorder the terms: 0 = 250 + 6.05x + -0.275x2 Solving 0 = 250 + 6.05x + -0.275x2 Solving for variable 'x'. Combine like terms: 0 + -250 = -250 -250 + -6.05x + 0.275x2 = 250 + 6.05x + -0.275x2 + -250 + -6.05x + 0.275x2 Reorder the terms: -250 + -6.05x + 0.275x2 = 250 + -250 + 6.05x + -6.05x + -0.275x2 + 0.275x2 Combine like terms: 250 + -250 = 0 -250 + -6.05x + 0.275x2 = 0 + 6.05x + -6.05x + -0.275x2 + 0.275x2 -250 + -6.05x + 0.275x2 = 6.05x + -6.05x + -0.275x2 + 0.275x2 Combine like terms: 6.05x + -6.05x = 0.00 -250 + -6.05x + 0.275x2 = 0.00 + -0.275x2 + 0.275x2 -250 + -6.05x + 0.275x2 = -0.275x2 + 0.275x2 Combine like terms: -0.275x2 + 0.275x2 = 0.000 -250 + -6.05x + 0.275x2 = 0.000 Begin completing the square. Divide all terms by 0.275 the coefficient of the squared term: Divide each side by '0.275'. -909.0909091 + -22x + x2 = 0 Move the constant term to the right: Add '909.0909091' to each side of the equation. -909.0909091 + -22x + 909.0909091 + x2 = 0 + 909.0909091 Reorder the terms: -909.0909091 + 909.0909091 + -22x + x2 = 0 + 909.0909091 Combine like terms: -909.0909091 + 909.0909091 = 0.0000000 0.0000000 + -22x + x2 = 0 + 909.0909091 -22x + x2 = 0 + 909.0909091 Combine like terms: 0 + 909.0909091 = 909.0909091 -22x + x2 = 909.0909091 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = 909.0909091 + 121 Reorder the terms: 121 + -22x + x2 = 909.0909091 + 121 Combine like terms: 909.0909091 + 121 = 1030.0909091 121 + -22x + x2 = 1030.0909091 Factor a perfect square on the left side: (x + -11)(x + -11) = 1030.0909091 Calculate the square root of the right side: 32.095029352 Break this problem into two subproblems by setting (x + -11) equal to 32.095029352 and -32.095029352.Subproblem 1
x + -11 = 32.095029352 Simplifying x + -11 = 32.095029352 Reorder the terms: -11 + x = 32.095029352 Solving -11 + x = 32.095029352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 32.095029352 + 11 Combine like terms: -11 + 11 = 0 0 + x = 32.095029352 + 11 x = 32.095029352 + 11 Combine like terms: 32.095029352 + 11 = 43.095029352 x = 43.095029352 Simplifying x = 43.095029352Subproblem 2
x + -11 = -32.095029352 Simplifying x + -11 = -32.095029352 Reorder the terms: -11 + x = -32.095029352 Solving -11 + x = -32.095029352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -32.095029352 + 11 Combine like terms: -11 + 11 = 0 0 + x = -32.095029352 + 11 x = -32.095029352 + 11 Combine like terms: -32.095029352 + 11 = -21.095029352 x = -21.095029352 Simplifying x = -21.095029352Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.095029352, -21.095029352}
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