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Simplifying 18x2 + -6400x + 400 = 0 Reorder the terms: 400 + -6400x + 18x2 = 0 Solving 400 + -6400x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(200 + -3200x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(200 + -3200x + 9x2)' equal to zero and attempt to solve: Simplifying 200 + -3200x + 9x2 = 0 Solving 200 + -3200x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 22.22222222 + -355.5555556x + x2 = 0 Move the constant term to the right: Add '-22.22222222' to each side of the equation. 22.22222222 + -355.5555556x + -22.22222222 + x2 = 0 + -22.22222222 Reorder the terms: 22.22222222 + -22.22222222 + -355.5555556x + x2 = 0 + -22.22222222 Combine like terms: 22.22222222 + -22.22222222 = 0.00000000 0.00000000 + -355.5555556x + x2 = 0 + -22.22222222 -355.5555556x + x2 = 0 + -22.22222222 Combine like terms: 0 + -22.22222222 = -22.22222222 -355.5555556x + x2 = -22.22222222 The x term is -355.5555556x. Take half its coefficient (-177.7777778). Square it (31604.93828) and add it to both sides. Add '31604.93828' to each side of the equation. -355.5555556x + 31604.93828 + x2 = -22.22222222 + 31604.93828 Reorder the terms: 31604.93828 + -355.5555556x + x2 = -22.22222222 + 31604.93828 Combine like terms: -22.22222222 + 31604.93828 = 31582.71605778 31604.93828 + -355.5555556x + x2 = 31582.71605778 Factor a perfect square on the left side: (x + -177.7777778)(x + -177.7777778) = 31582.71605778 Calculate the square root of the right side: 177.715266811 Break this problem into two subproblems by setting (x + -177.7777778) equal to 177.715266811 and -177.715266811.Subproblem 1
x + -177.7777778 = 177.715266811 Simplifying x + -177.7777778 = 177.715266811 Reorder the terms: -177.7777778 + x = 177.715266811 Solving -177.7777778 + x = 177.715266811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '177.7777778' to each side of the equation. -177.7777778 + 177.7777778 + x = 177.715266811 + 177.7777778 Combine like terms: -177.7777778 + 177.7777778 = 0.0000000 0.0000000 + x = 177.715266811 + 177.7777778 x = 177.715266811 + 177.7777778 Combine like terms: 177.715266811 + 177.7777778 = 355.493044611 x = 355.493044611 Simplifying x = 355.493044611Subproblem 2
x + -177.7777778 = -177.715266811 Simplifying x + -177.7777778 = -177.715266811 Reorder the terms: -177.7777778 + x = -177.715266811 Solving -177.7777778 + x = -177.715266811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '177.7777778' to each side of the equation. -177.7777778 + 177.7777778 + x = -177.715266811 + 177.7777778 Combine like terms: -177.7777778 + 177.7777778 = 0.0000000 0.0000000 + x = -177.715266811 + 177.7777778 x = -177.715266811 + 177.7777778 Combine like terms: -177.715266811 + 177.7777778 = 0.062510989 x = 0.062510989 Simplifying x = 0.062510989Solution
The solution to the problem is based on the solutions from the subproblems. x = {355.493044611, 0.062510989}Solution
x = {355.493044611, 0.062510989}
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