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Simplifying 100 = 2x2 + 6x + 9 Reorder the terms: 100 = 9 + 6x + 2x2 Solving 100 = 9 + 6x + 2x2 Solving for variable 'x'. Combine like terms: 100 + -9 = 91 91 + -6x + -2x2 = 9 + 6x + 2x2 + -9 + -6x + -2x2 Reorder the terms: 91 + -6x + -2x2 = 9 + -9 + 6x + -6x + 2x2 + -2x2 Combine like terms: 9 + -9 = 0 91 + -6x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2 91 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 91 + -6x + -2x2 = 0 + 2x2 + -2x2 91 + -6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 91 + -6x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -45.5 + 3x + x2 = 0 Move the constant term to the right: Add '45.5' to each side of the equation. -45.5 + 3x + 45.5 + x2 = 0 + 45.5 Reorder the terms: -45.5 + 45.5 + 3x + x2 = 0 + 45.5 Combine like terms: -45.5 + 45.5 = 0.0 0.0 + 3x + x2 = 0 + 45.5 3x + x2 = 0 + 45.5 Combine like terms: 0 + 45.5 = 45.5 3x + x2 = 45.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 45.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 45.5 + 2.25 Combine like terms: 45.5 + 2.25 = 47.75 2.25 + 3x + x2 = 47.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 47.75 Calculate the square root of the right side: 6.910137481 Break this problem into two subproblems by setting (x + 1.5) equal to 6.910137481 and -6.910137481.Subproblem 1
x + 1.5 = 6.910137481 Simplifying x + 1.5 = 6.910137481 Reorder the terms: 1.5 + x = 6.910137481 Solving 1.5 + x = 6.910137481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 6.910137481 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.910137481 + -1.5 x = 6.910137481 + -1.5 Combine like terms: 6.910137481 + -1.5 = 5.410137481 x = 5.410137481 Simplifying x = 5.410137481Subproblem 2
x + 1.5 = -6.910137481 Simplifying x + 1.5 = -6.910137481 Reorder the terms: 1.5 + x = -6.910137481 Solving 1.5 + x = -6.910137481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -6.910137481 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.910137481 + -1.5 x = -6.910137481 + -1.5 Combine like terms: -6.910137481 + -1.5 = -8.410137481 x = -8.410137481 Simplifying x = -8.410137481Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.410137481, -8.410137481}
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