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Simplifying 18x2 + -6400x + 400 = 274600 Reorder the terms: 400 + -6400x + 18x2 = 274600 Solving 400 + -6400x + 18x2 = 274600 Solving for variable 'x'. Reorder the terms: 400 + -274600 + -6400x + 18x2 = 274600 + -274600 Combine like terms: 400 + -274600 = -274200 -274200 + -6400x + 18x2 = 274600 + -274600 Combine like terms: 274600 + -274600 = 0 -274200 + -6400x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-137100 + -3200x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-137100 + -3200x + 9x2)' equal to zero and attempt to solve: Simplifying -137100 + -3200x + 9x2 = 0 Solving -137100 + -3200x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -15233.33333 + -355.5555556x + x2 = 0 Move the constant term to the right: Add '15233.33333' to each side of the equation. -15233.33333 + -355.5555556x + 15233.33333 + x2 = 0 + 15233.33333 Reorder the terms: -15233.33333 + 15233.33333 + -355.5555556x + x2 = 0 + 15233.33333 Combine like terms: -15233.33333 + 15233.33333 = 0.00000 0.00000 + -355.5555556x + x2 = 0 + 15233.33333 -355.5555556x + x2 = 0 + 15233.33333 Combine like terms: 0 + 15233.33333 = 15233.33333 -355.5555556x + x2 = 15233.33333 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 = 15233.33333 + 31604.93828 Reorder the terms: 31604.93828 + -355.5555556x + x2 = 15233.33333 + 31604.93828 Combine like terms: 15233.33333 + 31604.93828 = 46838.27161 31604.93828 + -355.5555556x + x2 = 46838.27161 Factor a perfect square on the left side: (x + -177.7777778)(x + -177.7777778) = 46838.27161 Calculate the square root of the right side: 216.421513741 Break this problem into two subproblems by setting (x + -177.7777778) equal to 216.421513741 and -216.421513741.Subproblem 1
x + -177.7777778 = 216.421513741 Simplifying x + -177.7777778 = 216.421513741 Reorder the terms: -177.7777778 + x = 216.421513741 Solving -177.7777778 + x = 216.421513741 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 = 216.421513741 + 177.7777778 Combine like terms: -177.7777778 + 177.7777778 = 0.0000000 0.0000000 + x = 216.421513741 + 177.7777778 x = 216.421513741 + 177.7777778 Combine like terms: 216.421513741 + 177.7777778 = 394.199291541 x = 394.199291541 Simplifying x = 394.199291541Subproblem 2
x + -177.7777778 = -216.421513741 Simplifying x + -177.7777778 = -216.421513741 Reorder the terms: -177.7777778 + x = -216.421513741 Solving -177.7777778 + x = -216.421513741 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 = -216.421513741 + 177.7777778 Combine like terms: -177.7777778 + 177.7777778 = 0.0000000 0.0000000 + x = -216.421513741 + 177.7777778 x = -216.421513741 + 177.7777778 Combine like terms: -216.421513741 + 177.7777778 = -38.643735941 x = -38.643735941 Simplifying x = -38.643735941Solution
The solution to the problem is based on the solutions from the subproblems. x = {394.199291541, -38.643735941}Solution
x = {394.199291541, -38.643735941}
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