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Simplifying 5x(x + 2) = 80 Reorder the terms: 5x(2 + x) = 80 (2 * 5x + x * 5x) = 80 (10x + 5x2) = 80 Solving 10x + 5x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + 10x + 5x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-16 + 2x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-16 + 2x + x2)' equal to zero and attempt to solve: Simplifying -16 + 2x + x2 = 0 Solving -16 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 2x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 2x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 2x + x2 = 0 + 16 2x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 2x + x2 = 16 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 = 16 + 1 Reorder the terms: 1 + 2x + x2 = 16 + 1 Combine like terms: 16 + 1 = 17 1 + 2x + x2 = 17 Factor a perfect square on the left side: (x + 1)(x + 1) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 1) equal to 4.123105626 and -4.123105626.Subproblem 1
x + 1 = 4.123105626 Simplifying x + 1 = 4.123105626 Reorder the terms: 1 + x = 4.123105626 Solving 1 + x = 4.123105626 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 = 4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.123105626 + -1 x = 4.123105626 + -1 Combine like terms: 4.123105626 + -1 = 3.123105626 x = 3.123105626 Simplifying x = 3.123105626Subproblem 2
x + 1 = -4.123105626 Simplifying x + 1 = -4.123105626 Reorder the terms: 1 + x = -4.123105626 Solving 1 + x = -4.123105626 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 = -4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.123105626 + -1 x = -4.123105626 + -1 Combine like terms: -4.123105626 + -1 = -5.123105626 x = -5.123105626 Simplifying x = -5.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.123105626, -5.123105626}Solution
x = {3.123105626, -5.123105626}
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