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Simplifying 0 = -125 + 20x + 0.44x2 Solving 0 = -125 + 20x + 0.44x2 Solving for variable 'x'. Combine like terms: 0 + 125 = 125 125 + -20x + -0.44x2 = -125 + 20x + 0.44x2 + 125 + -20x + -0.44x2 Reorder the terms: 125 + -20x + -0.44x2 = -125 + 125 + 20x + -20x + 0.44x2 + -0.44x2 Combine like terms: -125 + 125 = 0 125 + -20x + -0.44x2 = 0 + 20x + -20x + 0.44x2 + -0.44x2 125 + -20x + -0.44x2 = 20x + -20x + 0.44x2 + -0.44x2 Combine like terms: 20x + -20x = 0 125 + -20x + -0.44x2 = 0 + 0.44x2 + -0.44x2 125 + -20x + -0.44x2 = 0.44x2 + -0.44x2 Combine like terms: 0.44x2 + -0.44x2 = 0.00 125 + -20x + -0.44x2 = 0.00 Begin completing the square. Divide all terms by -0.44 the coefficient of the squared term: Divide each side by '-0.44'. -284.0909091 + 45.45454545x + x2 = 0 Move the constant term to the right: Add '284.0909091' to each side of the equation. -284.0909091 + 45.45454545x + 284.0909091 + x2 = 0 + 284.0909091 Reorder the terms: -284.0909091 + 284.0909091 + 45.45454545x + x2 = 0 + 284.0909091 Combine like terms: -284.0909091 + 284.0909091 = 0.0000000 0.0000000 + 45.45454545x + x2 = 0 + 284.0909091 45.45454545x + x2 = 0 + 284.0909091 Combine like terms: 0 + 284.0909091 = 284.0909091 45.45454545x + x2 = 284.0909091 The x term is 45.45454545x. Take half its coefficient (22.72727273). Square it (516.5289257) and add it to both sides. Add '516.5289257' to each side of the equation. 45.45454545x + 516.5289257 + x2 = 284.0909091 + 516.5289257 Reorder the terms: 516.5289257 + 45.45454545x + x2 = 284.0909091 + 516.5289257 Combine like terms: 284.0909091 + 516.5289257 = 800.6198348 516.5289257 + 45.45454545x + x2 = 800.6198348 Factor a perfect square on the left side: (x + 22.72727273)(x + 22.72727273) = 800.6198348 Calculate the square root of the right side: 28.295226361 Break this problem into two subproblems by setting (x + 22.72727273) equal to 28.295226361 and -28.295226361.Subproblem 1
x + 22.72727273 = 28.295226361 Simplifying x + 22.72727273 = 28.295226361 Reorder the terms: 22.72727273 + x = 28.295226361 Solving 22.72727273 + x = 28.295226361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.72727273' to each side of the equation. 22.72727273 + -22.72727273 + x = 28.295226361 + -22.72727273 Combine like terms: 22.72727273 + -22.72727273 = 0.00000000 0.00000000 + x = 28.295226361 + -22.72727273 x = 28.295226361 + -22.72727273 Combine like terms: 28.295226361 + -22.72727273 = 5.567953631 x = 5.567953631 Simplifying x = 5.567953631Subproblem 2
x + 22.72727273 = -28.295226361 Simplifying x + 22.72727273 = -28.295226361 Reorder the terms: 22.72727273 + x = -28.295226361 Solving 22.72727273 + x = -28.295226361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.72727273' to each side of the equation. 22.72727273 + -22.72727273 + x = -28.295226361 + -22.72727273 Combine like terms: 22.72727273 + -22.72727273 = 0.00000000 0.00000000 + x = -28.295226361 + -22.72727273 x = -28.295226361 + -22.72727273 Combine like terms: -28.295226361 + -22.72727273 = -51.022499091 x = -51.022499091 Simplifying x = -51.022499091Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.567953631, -51.022499091}
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