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Simplifying 5(x2 + 8x + 16) = 60 Reorder the terms: 5(16 + 8x + x2) = 60 (16 * 5 + 8x * 5 + x2 * 5) = 60 (80 + 40x + 5x2) = 60 Solving 80 + 40x + 5x2 = 60 Solving for variable 'x'. Reorder the terms: 80 + -60 + 40x + 5x2 = 60 + -60 Combine like terms: 80 + -60 = 20 20 + 40x + 5x2 = 60 + -60 Combine like terms: 60 + -60 = 0 20 + 40x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(4 + 8x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + 8x + x2)' equal to zero and attempt to solve: Simplifying 4 + 8x + x2 = 0 Solving 4 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 8x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 8x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 8x + x2 = 0 + -4 8x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 8x + x2 = -4 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 = -4 + 16 Reorder the terms: 16 + 8x + x2 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + 8x + x2 = 12 Factor a perfect square on the left side: (x + 4)(x + 4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 4) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 4 = 3.464101615 Simplifying x + 4 = 3.464101615 Reorder the terms: 4 + x = 3.464101615 Solving 4 + x = 3.464101615 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 = 3.464101615 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.464101615 + -4 x = 3.464101615 + -4 Combine like terms: 3.464101615 + -4 = -0.535898385 x = -0.535898385 Simplifying x = -0.535898385Subproblem 2
x + 4 = -3.464101615 Simplifying x + 4 = -3.464101615 Reorder the terms: 4 + x = -3.464101615 Solving 4 + x = -3.464101615 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 = -3.464101615 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.464101615 + -4 x = -3.464101615 + -4 Combine like terms: -3.464101615 + -4 = -7.464101615 x = -7.464101615 Simplifying x = -7.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.535898385, -7.464101615}Solution
x = {-0.535898385, -7.464101615}
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