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Simplifying 12x2 + -78x + 93.5 = 0 Reorder the terms: 93.5 + -78x + 12x2 = 0 Solving 93.5 + -78x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 7.791666667 + -6.5x + x2 = 0 Move the constant term to the right: Add '-7.791666667' to each side of the equation. 7.791666667 + -6.5x + -7.791666667 + x2 = 0 + -7.791666667 Reorder the terms: 7.791666667 + -7.791666667 + -6.5x + x2 = 0 + -7.791666667 Combine like terms: 7.791666667 + -7.791666667 = 0.000000000 0.000000000 + -6.5x + x2 = 0 + -7.791666667 -6.5x + x2 = 0 + -7.791666667 Combine like terms: 0 + -7.791666667 = -7.791666667 -6.5x + x2 = -7.791666667 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = -7.791666667 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -7.791666667 + 10.5625 Combine like terms: -7.791666667 + 10.5625 = 2.770833333 10.5625 + -6.5x + x2 = 2.770833333 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 2.770833333 Calculate the square root of the right side: 1.66458203 Break this problem into two subproblems by setting (x + -3.25) equal to 1.66458203 and -1.66458203.Subproblem 1
x + -3.25 = 1.66458203 Simplifying x + -3.25 = 1.66458203 Reorder the terms: -3.25 + x = 1.66458203 Solving -3.25 + x = 1.66458203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 1.66458203 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 1.66458203 + 3.25 x = 1.66458203 + 3.25 Combine like terms: 1.66458203 + 3.25 = 4.91458203 x = 4.91458203 Simplifying x = 4.91458203Subproblem 2
x + -3.25 = -1.66458203 Simplifying x + -3.25 = -1.66458203 Reorder the terms: -3.25 + x = -1.66458203 Solving -3.25 + x = -1.66458203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -1.66458203 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -1.66458203 + 3.25 x = -1.66458203 + 3.25 Combine like terms: -1.66458203 + 3.25 = 1.58541797 x = 1.58541797 Simplifying x = 1.58541797Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.91458203, 1.58541797}
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