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Simplifying 5x2 + 40x + -180 = 0 Reorder the terms: -180 + 40x + 5x2 = 0 Solving -180 + 40x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-36 + 8x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-36 + 8x + x2)' equal to zero and attempt to solve: Simplifying -36 + 8x + x2 = 0 Solving -36 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 8x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 8x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 8x + x2 = 0 + 36 8x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 8x + x2 = 36 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 36 + 16 Reorder the terms: 16 + 8x + x2 = 36 + 16 Combine like terms: 36 + 16 = 52 16 + 8x + x2 = 52 Factor a perfect square on the left side: (x + 4)(x + 4) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + 4) equal to 7.211102551 and -7.211102551.Subproblem 1
x + 4 = 7.211102551 Simplifying x + 4 = 7.211102551 Reorder the terms: 4 + x = 7.211102551 Solving 4 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 7.211102551 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.211102551 + -4 x = 7.211102551 + -4 Combine like terms: 7.211102551 + -4 = 3.211102551 x = 3.211102551 Simplifying x = 3.211102551Subproblem 2
x + 4 = -7.211102551 Simplifying x + 4 = -7.211102551 Reorder the terms: 4 + x = -7.211102551 Solving 4 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -7.211102551 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.211102551 + -4 x = -7.211102551 + -4 Combine like terms: -7.211102551 + -4 = -11.211102551 x = -11.211102551 Simplifying x = -11.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.211102551, -11.211102551}Solution
x = {3.211102551, -11.211102551}
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