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Simplifying 80x + -36 + -4x2 = 48 Reorder the terms: -36 + 80x + -4x2 = 48 Solving -36 + 80x + -4x2 = 48 Solving for variable 'x'. Reorder the terms: -36 + -48 + 80x + -4x2 = 48 + -48 Combine like terms: -36 + -48 = -84 -84 + 80x + -4x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -84 + 80x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-21 + 20x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-21 + 20x + -1x2)' equal to zero and attempt to solve: Simplifying -21 + 20x + -1x2 = 0 Solving -21 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 21 + -20x + x2 = 0 Move the constant term to the right: Add '-21' to each side of the equation. 21 + -20x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -20x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -20x + x2 = 0 + -21 -20x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -20x + x2 = -21 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -21 + 100 Reorder the terms: 100 + -20x + x2 = -21 + 100 Combine like terms: -21 + 100 = 79 100 + -20x + x2 = 79 Factor a perfect square on the left side: (x + -10)(x + -10) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + -10) equal to 8.888194417 and -8.888194417.Subproblem 1
x + -10 = 8.888194417 Simplifying x + -10 = 8.888194417 Reorder the terms: -10 + x = 8.888194417 Solving -10 + x = 8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 8.888194417 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.888194417 + 10 x = 8.888194417 + 10 Combine like terms: 8.888194417 + 10 = 18.888194417 x = 18.888194417 Simplifying x = 18.888194417Subproblem 2
x + -10 = -8.888194417 Simplifying x + -10 = -8.888194417 Reorder the terms: -10 + x = -8.888194417 Solving -10 + x = -8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -8.888194417 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.888194417 + 10 x = -8.888194417 + 10 Combine like terms: -8.888194417 + 10 = 1.111805583 x = 1.111805583 Simplifying x = 1.111805583Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.888194417, 1.111805583}Solution
x = {18.888194417, 1.111805583}
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