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Simplifying 0 = 2x2 + 28x + -3840 Reorder the terms: 0 = -3840 + 28x + 2x2 Solving 0 = -3840 + 28x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 3840 = 3840 3840 + -28x + -2x2 = -3840 + 28x + 2x2 + 3840 + -28x + -2x2 Reorder the terms: 3840 + -28x + -2x2 = -3840 + 3840 + 28x + -28x + 2x2 + -2x2 Combine like terms: -3840 + 3840 = 0 3840 + -28x + -2x2 = 0 + 28x + -28x + 2x2 + -2x2 3840 + -28x + -2x2 = 28x + -28x + 2x2 + -2x2 Combine like terms: 28x + -28x = 0 3840 + -28x + -2x2 = 0 + 2x2 + -2x2 3840 + -28x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 3840 + -28x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1920 + -14x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1920 + -14x + -1x2)' equal to zero and attempt to solve: Simplifying 1920 + -14x + -1x2 = 0 Solving 1920 + -14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1920 + 14x + x2 = 0 Move the constant term to the right: Add '1920' to each side of the equation. -1920 + 14x + 1920 + x2 = 0 + 1920 Reorder the terms: -1920 + 1920 + 14x + x2 = 0 + 1920 Combine like terms: -1920 + 1920 = 0 0 + 14x + x2 = 0 + 1920 14x + x2 = 0 + 1920 Combine like terms: 0 + 1920 = 1920 14x + x2 = 1920 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 1920 + 49 Reorder the terms: 49 + 14x + x2 = 1920 + 49 Combine like terms: 1920 + 49 = 1969 49 + 14x + x2 = 1969 Factor a perfect square on the left side: (x + 7)(x + 7) = 1969 Calculate the square root of the right side: 44.373415465 Break this problem into two subproblems by setting (x + 7) equal to 44.373415465 and -44.373415465.Subproblem 1
x + 7 = 44.373415465 Simplifying x + 7 = 44.373415465 Reorder the terms: 7 + x = 44.373415465 Solving 7 + x = 44.373415465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 44.373415465 + -7 Combine like terms: 7 + -7 = 0 0 + x = 44.373415465 + -7 x = 44.373415465 + -7 Combine like terms: 44.373415465 + -7 = 37.373415465 x = 37.373415465 Simplifying x = 37.373415465Subproblem 2
x + 7 = -44.373415465 Simplifying x + 7 = -44.373415465 Reorder the terms: 7 + x = -44.373415465 Solving 7 + x = -44.373415465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -44.373415465 + -7 Combine like terms: 7 + -7 = 0 0 + x = -44.373415465 + -7 x = -44.373415465 + -7 Combine like terms: -44.373415465 + -7 = -51.373415465 x = -51.373415465 Simplifying x = -51.373415465Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.373415465, -51.373415465}Solution
x = {37.373415465, -51.373415465}
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