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Simplifying 4x2 + -120x + -40x + 1200 = 684 Reorder the terms: 1200 + -120x + -40x + 4x2 = 684 Combine like terms: -120x + -40x = -160x 1200 + -160x + 4x2 = 684 Solving 1200 + -160x + 4x2 = 684 Solving for variable 'x'. Reorder the terms: 1200 + -684 + -160x + 4x2 = 684 + -684 Combine like terms: 1200 + -684 = 516 516 + -160x + 4x2 = 684 + -684 Combine like terms: 684 + -684 = 0 516 + -160x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(129 + -40x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(129 + -40x + x2)' equal to zero and attempt to solve: Simplifying 129 + -40x + x2 = 0 Solving 129 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-129' to each side of the equation. 129 + -40x + -129 + x2 = 0 + -129 Reorder the terms: 129 + -129 + -40x + x2 = 0 + -129 Combine like terms: 129 + -129 = 0 0 + -40x + x2 = 0 + -129 -40x + x2 = 0 + -129 Combine like terms: 0 + -129 = -129 -40x + x2 = -129 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -129 + 400 Reorder the terms: 400 + -40x + x2 = -129 + 400 Combine like terms: -129 + 400 = 271 400 + -40x + x2 = 271 Factor a perfect square on the left side: (x + -20)(x + -20) = 271 Calculate the square root of the right side: 16.462077633 Break this problem into two subproblems by setting (x + -20) equal to 16.462077633 and -16.462077633.Subproblem 1
x + -20 = 16.462077633 Simplifying x + -20 = 16.462077633 Reorder the terms: -20 + x = 16.462077633 Solving -20 + x = 16.462077633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 16.462077633 + 20 Combine like terms: -20 + 20 = 0 0 + x = 16.462077633 + 20 x = 16.462077633 + 20 Combine like terms: 16.462077633 + 20 = 36.462077633 x = 36.462077633 Simplifying x = 36.462077633Subproblem 2
x + -20 = -16.462077633 Simplifying x + -20 = -16.462077633 Reorder the terms: -20 + x = -16.462077633 Solving -20 + x = -16.462077633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -16.462077633 + 20 Combine like terms: -20 + 20 = 0 0 + x = -16.462077633 + 20 x = -16.462077633 + 20 Combine like terms: -16.462077633 + 20 = 3.537922367 x = 3.537922367 Simplifying x = 3.537922367Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.462077633, 3.537922367}Solution
x = {36.462077633, 3.537922367}
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