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Simplifying 3x2 + -5x2 + -48x + 80 = 0 Reorder the terms: 80 + -48x + 3x2 + -5x2 = 0 Combine like terms: 3x2 + -5x2 = -2x2 80 + -48x + -2x2 = 0 Solving 80 + -48x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(40 + -24x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + -24x + -1x2)' equal to zero and attempt to solve: Simplifying 40 + -24x + -1x2 = 0 Solving 40 + -24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 24x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 24x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 24x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 24x + x2 = 0 + 40 24x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 24x + x2 = 40 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 40 + 144 Reorder the terms: 144 + 24x + x2 = 40 + 144 Combine like terms: 40 + 144 = 184 144 + 24x + x2 = 184 Factor a perfect square on the left side: (x + 12)(x + 12) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (x + 12) equal to 13.564659966 and -13.564659966.Subproblem 1
x + 12 = 13.564659966 Simplifying x + 12 = 13.564659966 Reorder the terms: 12 + x = 13.564659966 Solving 12 + x = 13.564659966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 13.564659966 + -12 Combine like terms: 12 + -12 = 0 0 + x = 13.564659966 + -12 x = 13.564659966 + -12 Combine like terms: 13.564659966 + -12 = 1.564659966 x = 1.564659966 Simplifying x = 1.564659966Subproblem 2
x + 12 = -13.564659966 Simplifying x + 12 = -13.564659966 Reorder the terms: 12 + x = -13.564659966 Solving 12 + x = -13.564659966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -13.564659966 + -12 Combine like terms: 12 + -12 = 0 0 + x = -13.564659966 + -12 x = -13.564659966 + -12 Combine like terms: -13.564659966 + -12 = -25.564659966 x = -25.564659966 Simplifying x = -25.564659966Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.564659966, -25.564659966}Solution
x = {1.564659966, -25.564659966}
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