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Simplifying 20x + 150 + -1x2 = 0 Reorder the terms: 150 + 20x + -1x2 = 0 Solving 150 + 20x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -150 + -20x + x2 = 0 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 = 25.811388301 x = 25.811388301 Simplifying x = 25.811388301Subproblem 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 = -5.811388301 x = -5.811388301 Simplifying x = -5.811388301Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.811388301, -5.811388301}
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