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Simplifying 100 = x2 + -12x + 45 Reorder the terms: 100 = 45 + -12x + x2 Solving 100 = 45 + -12x + x2 Solving for variable 'x'. Combine like terms: 100 + -45 = 55 55 + 12x + -1x2 = 45 + -12x + x2 + -45 + 12x + -1x2 Reorder the terms: 55 + 12x + -1x2 = 45 + -45 + -12x + 12x + x2 + -1x2 Combine like terms: 45 + -45 = 0 55 + 12x + -1x2 = 0 + -12x + 12x + x2 + -1x2 55 + 12x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 55 + 12x + -1x2 = 0 + x2 + -1x2 55 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 55 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -55 + -12x + x2 = 0 Move the constant term to the right: Add '55' to each side of the equation. -55 + -12x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + -12x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -12x + x2 = 0 + 55 -12x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 -12x + x2 = 55 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 55 + 36 Reorder the terms: 36 + -12x + x2 = 55 + 36 Combine like terms: 55 + 36 = 91 36 + -12x + x2 = 91 Factor a perfect square on the left side: (x + -6)(x + -6) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + -6) equal to 9.539392014 and -9.539392014.Subproblem 1
x + -6 = 9.539392014 Simplifying x + -6 = 9.539392014 Reorder the terms: -6 + x = 9.539392014 Solving -6 + x = 9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 9.539392014 + 6 Combine like terms: -6 + 6 = 0 0 + x = 9.539392014 + 6 x = 9.539392014 + 6 Combine like terms: 9.539392014 + 6 = 15.539392014 x = 15.539392014 Simplifying x = 15.539392014Subproblem 2
x + -6 = -9.539392014 Simplifying x + -6 = -9.539392014 Reorder the terms: -6 + x = -9.539392014 Solving -6 + x = -9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -9.539392014 + 6 Combine like terms: -6 + 6 = 0 0 + x = -9.539392014 + 6 x = -9.539392014 + 6 Combine like terms: -9.539392014 + 6 = -3.539392014 x = -3.539392014 Simplifying x = -3.539392014Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.539392014, -3.539392014}
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