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Simplifying 4x2 + 12x + 9 = 180 Reorder the terms: 9 + 12x + 4x2 = 180 Solving 9 + 12x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: 9 + -180 + 12x + 4x2 = 180 + -180 Combine like terms: 9 + -180 = -171 -171 + 12x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -171 + 12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -42.75 + 3x + x2 = 0 Move the constant term to the right: Add '42.75' to each side of the equation. -42.75 + 3x + 42.75 + x2 = 0 + 42.75 Reorder the terms: -42.75 + 42.75 + 3x + x2 = 0 + 42.75 Combine like terms: -42.75 + 42.75 = 0.00 0.00 + 3x + x2 = 0 + 42.75 3x + x2 = 0 + 42.75 Combine like terms: 0 + 42.75 = 42.75 3x + x2 = 42.75 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 = 42.75 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 42.75 + 2.25 Combine like terms: 42.75 + 2.25 = 45 2.25 + 3x + x2 = 45 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + 1.5) equal to 6.708203933 and -6.708203933.Subproblem 1
x + 1.5 = 6.708203933 Simplifying x + 1.5 = 6.708203933 Reorder the terms: 1.5 + x = 6.708203933 Solving 1.5 + x = 6.708203933 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 = 6.708203933 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.708203933 + -1.5 x = 6.708203933 + -1.5 Combine like terms: 6.708203933 + -1.5 = 5.208203933 x = 5.208203933 Simplifying x = 5.208203933Subproblem 2
x + 1.5 = -6.708203933 Simplifying x + 1.5 = -6.708203933 Reorder the terms: 1.5 + x = -6.708203933 Solving 1.5 + x = -6.708203933 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 = -6.708203933 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.708203933 + -1.5 x = -6.708203933 + -1.5 Combine like terms: -6.708203933 + -1.5 = -8.208203933 x = -8.208203933 Simplifying x = -8.208203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.208203933, -8.208203933}
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