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Simplifying 6400 + -3x + -1x2 = 0 Solving 6400 + -3x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6400 + 3x + x2 = 0 Move the constant term to the right: Add '6400' to each side of the equation. -6400 + 3x + 6400 + x2 = 0 + 6400 Reorder the terms: -6400 + 6400 + 3x + x2 = 0 + 6400 Combine like terms: -6400 + 6400 = 0 0 + 3x + x2 = 0 + 6400 3x + x2 = 0 + 6400 Combine like terms: 0 + 6400 = 6400 3x + x2 = 6400 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 6400 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 6400 + 2.25 Combine like terms: 6400 + 2.25 = 6402.25 2.25 + 3x + x2 = 6402.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 6402.25 Calculate the square root of the right side: 80.014061264 Break this problem into two subproblems by setting (x + 1.5) equal to 80.014061264 and -80.014061264.Subproblem 1
x + 1.5 = 80.014061264 Simplifying x + 1.5 = 80.014061264 Reorder the terms: 1.5 + x = 80.014061264 Solving 1.5 + x = 80.014061264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 80.014061264 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 80.014061264 + -1.5 x = 80.014061264 + -1.5 Combine like terms: 80.014061264 + -1.5 = 78.514061264 x = 78.514061264 Simplifying x = 78.514061264Subproblem 2
x + 1.5 = -80.014061264 Simplifying x + 1.5 = -80.014061264 Reorder the terms: 1.5 + x = -80.014061264 Solving 1.5 + x = -80.014061264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -80.014061264 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -80.014061264 + -1.5 x = -80.014061264 + -1.5 Combine like terms: -80.014061264 + -1.5 = -81.514061264 x = -81.514061264 Simplifying x = -81.514061264Solution
The solution to the problem is based on the solutions from the subproblems. x = {78.514061264, -81.514061264}
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