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Simplifying x2 + -12x + 45 = 100 Reorder the terms: 45 + -12x + x2 = 100 Solving 45 + -12x + x2 = 100 Solving for variable 'x'. Reorder the terms: 45 + -100 + -12x + x2 = 100 + -100 Combine like terms: 45 + -100 = -55 -55 + -12x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -55 + -12x + x2 = 0 Begin completing the square. 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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