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Simplifying 5x(x + 2) = 100 Reorder the terms: 5x(2 + x) = 100 (2 * 5x + x * 5x) = 100 (10x + 5x2) = 100 Solving 10x + 5x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 10x + 5x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + 2x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-20 + 2x + x2)' equal to zero and attempt to solve: Simplifying -20 + 2x + x2 = 0 Solving -20 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 2x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 2x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 2x + x2 = 0 + 20 2x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 2x + x2 = 20 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 = 20 + 1 Reorder the terms: 1 + 2x + x2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + 2x + x2 = 21 Factor a perfect square on the left side: (x + 1)(x + 1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + 1) equal to 4.582575695 and -4.582575695.Subproblem 1
x + 1 = 4.582575695 Simplifying x + 1 = 4.582575695 Reorder the terms: 1 + x = 4.582575695 Solving 1 + x = 4.582575695 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 = 4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.582575695 + -1 x = 4.582575695 + -1 Combine like terms: 4.582575695 + -1 = 3.582575695 x = 3.582575695 Simplifying x = 3.582575695Subproblem 2
x + 1 = -4.582575695 Simplifying x + 1 = -4.582575695 Reorder the terms: 1 + x = -4.582575695 Solving 1 + x = -4.582575695 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 = -4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.582575695 + -1 x = -4.582575695 + -1 Combine like terms: -4.582575695 + -1 = -5.582575695 x = -5.582575695 Simplifying x = -5.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.582575695, -5.582575695}Solution
x = {3.582575695, -5.582575695}
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