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Simplifying 2x2 + 4x(x + 3) = 180 Reorder the terms: 2x2 + 4x(3 + x) = 180 2x2 + (3 * 4x + x * 4x) = 180 2x2 + (12x + 4x2) = 180 Reorder the terms: 12x + 2x2 + 4x2 = 180 Combine like terms: 2x2 + 4x2 = 6x2 12x + 6x2 = 180 Solving 12x + 6x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 12x + 6x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-30 + 2x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-30 + 2x + x2)' equal to zero and attempt to solve: Simplifying -30 + 2x + x2 = 0 Solving -30 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 2x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 2x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 2x + x2 = 0 + 30 2x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 2x + x2 = 30 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 30 + 1 Reorder the terms: 1 + 2x + x2 = 30 + 1 Combine like terms: 30 + 1 = 31 1 + 2x + x2 = 31 Factor a perfect square on the left side: (x + 1)(x + 1) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + 1) equal to 5.567764363 and -5.567764363.Subproblem 1
x + 1 = 5.567764363 Simplifying x + 1 = 5.567764363 Reorder the terms: 1 + x = 5.567764363 Solving 1 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.567764363 + -1 x = 5.567764363 + -1 Combine like terms: 5.567764363 + -1 = 4.567764363 x = 4.567764363 Simplifying x = 4.567764363Subproblem 2
x + 1 = -5.567764363 Simplifying x + 1 = -5.567764363 Reorder the terms: 1 + x = -5.567764363 Solving 1 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.567764363 + -1 x = -5.567764363 + -1 Combine like terms: -5.567764363 + -1 = -6.567764363 x = -6.567764363 Simplifying x = -6.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.567764363, -6.567764363}Solution
x = {4.567764363, -6.567764363}
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