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Simplifying 0.5x2 + 4116 = 91x Reorder the terms: 4116 + 0.5x2 = 91x Solving 4116 + 0.5x2 = 91x Solving for variable 'x'. Reorder the terms: 4116 + -91x + 0.5x2 = 91x + -91x Combine like terms: 91x + -91x = 0 4116 + -91x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 8232 + -182x + x2 = 0 Move the constant term to the right: Add '-8232' to each side of the equation. 8232 + -182x + -8232 + x2 = 0 + -8232 Reorder the terms: 8232 + -8232 + -182x + x2 = 0 + -8232 Combine like terms: 8232 + -8232 = 0 0 + -182x + x2 = 0 + -8232 -182x + x2 = 0 + -8232 Combine like terms: 0 + -8232 = -8232 -182x + x2 = -8232 The x term is -182x. Take half its coefficient (-91). Square it (8281) and add it to both sides. Add '8281' to each side of the equation. -182x + 8281 + x2 = -8232 + 8281 Reorder the terms: 8281 + -182x + x2 = -8232 + 8281 Combine like terms: -8232 + 8281 = 49 8281 + -182x + x2 = 49 Factor a perfect square on the left side: (x + -91)(x + -91) = 49 Calculate the square root of the right side: 7 Break this problem into two subproblems by setting (x + -91) equal to 7 and -7.Subproblem 1
x + -91 = 7 Simplifying x + -91 = 7 Reorder the terms: -91 + x = 7 Solving -91 + x = 7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '91' to each side of the equation. -91 + 91 + x = 7 + 91 Combine like terms: -91 + 91 = 0 0 + x = 7 + 91 x = 7 + 91 Combine like terms: 7 + 91 = 98 x = 98 Simplifying x = 98Subproblem 2
x + -91 = -7 Simplifying x + -91 = -7 Reorder the terms: -91 + x = -7 Solving -91 + x = -7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '91' to each side of the equation. -91 + 91 + x = -7 + 91 Combine like terms: -91 + 91 = 0 0 + x = -7 + 91 x = -7 + 91 Combine like terms: -7 + 91 = 84 x = 84 Simplifying x = 84Solution
The solution to the problem is based on the solutions from the subproblems. x = {98, 84}
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