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Simplifying (3x + 8) + 4x(x + 4) = 180 Reorder the terms: (8 + 3x) + 4x(x + 4) = 180 Remove parenthesis around (8 + 3x) 8 + 3x + 4x(x + 4) = 180 Reorder the terms: 8 + 3x + 4x(4 + x) = 180 8 + 3x + (4 * 4x + x * 4x) = 180 8 + 3x + (16x + 4x2) = 180 Combine like terms: 3x + 16x = 19x 8 + 19x + 4x2 = 180 Solving 8 + 19x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: 8 + -180 + 19x + 4x2 = 180 + -180 Combine like terms: 8 + -180 = -172 -172 + 19x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -172 + 19x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -43 + 4.75x + x2 = 0 Move the constant term to the right: Add '43' to each side of the equation. -43 + 4.75x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + 4.75x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 4.75x + x2 = 0 + 43 4.75x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 4.75x + x2 = 43 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = 43 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 43 + 5.640625 Combine like terms: 43 + 5.640625 = 48.640625 5.640625 + 4.75x + x2 = 48.640625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 48.640625 Calculate the square root of the right side: 6.974283117 Break this problem into two subproblems by setting (x + 2.375) equal to 6.974283117 and -6.974283117.Subproblem 1
x + 2.375 = 6.974283117 Simplifying x + 2.375 = 6.974283117 Reorder the terms: 2.375 + x = 6.974283117 Solving 2.375 + x = 6.974283117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 6.974283117 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 6.974283117 + -2.375 x = 6.974283117 + -2.375 Combine like terms: 6.974283117 + -2.375 = 4.599283117 x = 4.599283117 Simplifying x = 4.599283117Subproblem 2
x + 2.375 = -6.974283117 Simplifying x + 2.375 = -6.974283117 Reorder the terms: 2.375 + x = -6.974283117 Solving 2.375 + x = -6.974283117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -6.974283117 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -6.974283117 + -2.375 x = -6.974283117 + -2.375 Combine like terms: -6.974283117 + -2.375 = -9.349283117 x = -9.349283117 Simplifying x = -9.349283117Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.599283117, -9.349283117}
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