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Simplifying 144x + -16x2 = 244 Solving 144x + -16x2 = 244 Solving for variable 'x'. Reorder the terms: -244 + 144x + -16x2 = 244 + -244 Combine like terms: 244 + -244 = 0 -244 + 144x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-61 + 36x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-61 + 36x + -4x2)' equal to zero and attempt to solve: Simplifying -61 + 36x + -4x2 = 0 Solving -61 + 36x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 15.25 + -9x + x2 = 0 Move the constant term to the right: Add '-15.25' to each side of the equation. 15.25 + -9x + -15.25 + x2 = 0 + -15.25 Reorder the terms: 15.25 + -15.25 + -9x + x2 = 0 + -15.25 Combine like terms: 15.25 + -15.25 = 0.00 0.00 + -9x + x2 = 0 + -15.25 -9x + x2 = 0 + -15.25 Combine like terms: 0 + -15.25 = -15.25 -9x + x2 = -15.25 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -15.25 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -15.25 + 20.25 Combine like terms: -15.25 + 20.25 = 5 20.25 + -9x + x2 = 5 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -4.5) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -4.5 = 2.236067978 Simplifying x + -4.5 = 2.236067978 Reorder the terms: -4.5 + x = 2.236067978 Solving -4.5 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 2.236067978 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 2.236067978 + 4.5 x = 2.236067978 + 4.5 Combine like terms: 2.236067978 + 4.5 = 6.736067978 x = 6.736067978 Simplifying x = 6.736067978Subproblem 2
x + -4.5 = -2.236067978 Simplifying x + -4.5 = -2.236067978 Reorder the terms: -4.5 + x = -2.236067978 Solving -4.5 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -2.236067978 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -2.236067978 + 4.5 x = -2.236067978 + 4.5 Combine like terms: -2.236067978 + 4.5 = 2.263932022 x = 2.263932022 Simplifying x = 2.263932022Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.736067978, 2.263932022}Solution
x = {6.736067978, 2.263932022}
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