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Simplifying 4x2 + 80x = 768 Reorder the terms: 80x + 4x2 = 768 Solving 80x + 4x2 = 768 Solving for variable 'x'. Reorder the terms: -768 + 80x + 4x2 = 768 + -768 Combine like terms: 768 + -768 = 0 -768 + 80x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-192 + 20x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-192 + 20x + x2)' equal to zero and attempt to solve: Simplifying -192 + 20x + x2 = 0 Solving -192 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + 20x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 20x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 20x + x2 = 0 + 192 20x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 20x + x2 = 192 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 = 192 + 100 Reorder the terms: 100 + 20x + x2 = 192 + 100 Combine like terms: 192 + 100 = 292 100 + 20x + x2 = 292 Factor a perfect square on the left side: (x + 10)(x + 10) = 292 Calculate the square root of the right side: 17.088007491 Break this problem into two subproblems by setting (x + 10) equal to 17.088007491 and -17.088007491.Subproblem 1
x + 10 = 17.088007491 Simplifying x + 10 = 17.088007491 Reorder the terms: 10 + x = 17.088007491 Solving 10 + x = 17.088007491 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 = 17.088007491 + -10 Combine like terms: 10 + -10 = 0 0 + x = 17.088007491 + -10 x = 17.088007491 + -10 Combine like terms: 17.088007491 + -10 = 7.088007491 x = 7.088007491 Simplifying x = 7.088007491Subproblem 2
x + 10 = -17.088007491 Simplifying x + 10 = -17.088007491 Reorder the terms: 10 + x = -17.088007491 Solving 10 + x = -17.088007491 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 = -17.088007491 + -10 Combine like terms: 10 + -10 = 0 0 + x = -17.088007491 + -10 x = -17.088007491 + -10 Combine like terms: -17.088007491 + -10 = -27.088007491 x = -27.088007491 Simplifying x = -27.088007491Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.088007491, -27.088007491}Solution
x = {7.088007491, -27.088007491}
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