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Simplifying 5x2 + 12x + -80 = 0 Reorder the terms: -80 + 12x + 5x2 = 0 Solving -80 + 12x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -16 + 2.4x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 2.4x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 2.4x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 2.4x + x2 = 0 + 16 2.4x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 2.4x + x2 = 16 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 16 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 16 + 1.44 Combine like terms: 16 + 1.44 = 17.44 1.44 + 2.4x + x2 = 17.44 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 17.44 Calculate the square root of the right side: 4.176122604 Break this problem into two subproblems by setting (x + 1.2) equal to 4.176122604 and -4.176122604.Subproblem 1
x + 1.2 = 4.176122604 Simplifying x + 1.2 = 4.176122604 Reorder the terms: 1.2 + x = 4.176122604 Solving 1.2 + x = 4.176122604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 4.176122604 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 4.176122604 + -1.2 x = 4.176122604 + -1.2 Combine like terms: 4.176122604 + -1.2 = 2.976122604 x = 2.976122604 Simplifying x = 2.976122604Subproblem 2
x + 1.2 = -4.176122604 Simplifying x + 1.2 = -4.176122604 Reorder the terms: 1.2 + x = -4.176122604 Solving 1.2 + x = -4.176122604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -4.176122604 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -4.176122604 + -1.2 x = -4.176122604 + -1.2 Combine like terms: -4.176122604 + -1.2 = -5.376122604 x = -5.376122604 Simplifying x = -5.376122604Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.976122604, -5.376122604}
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