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Simplifying x2 + 20x = 150 Reorder the terms: 20x + x2 = 150 Solving 20x + x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 20x + x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + 20x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 20x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 20x + x2 = 0 + 150 20x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 20x + x2 = 150 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 150 + 100 Reorder the terms: 100 + 20x + x2 = 150 + 100 Combine like terms: 150 + 100 = 250 100 + 20x + x2 = 250 Factor a perfect square on the left side: (x + 10)(x + 10) = 250 Calculate the square root of the right side: 15.811388301 Break this problem into two subproblems by setting (x + 10) equal to 15.811388301 and -15.811388301.Subproblem 1
x + 10 = 15.811388301 Simplifying x + 10 = 15.811388301 Reorder the terms: 10 + x = 15.811388301 Solving 10 + x = 15.811388301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 15.811388301 + -10 Combine like terms: 10 + -10 = 0 0 + x = 15.811388301 + -10 x = 15.811388301 + -10 Combine like terms: 15.811388301 + -10 = 5.811388301 x = 5.811388301 Simplifying x = 5.811388301Subproblem 2
x + 10 = -15.811388301 Simplifying x + 10 = -15.811388301 Reorder the terms: 10 + x = -15.811388301 Solving 10 + x = -15.811388301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -15.811388301 + -10 Combine like terms: 10 + -10 = 0 0 + x = -15.811388301 + -10 x = -15.811388301 + -10 Combine like terms: -15.811388301 + -10 = -25.811388301 x = -25.811388301 Simplifying x = -25.811388301Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.811388301, -25.811388301}
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