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Simplifying 5x2 + 7x + -80 = 0 Reorder the terms: -80 + 7x + 5x2 = 0 Solving -80 + 7x + 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 + 1.4x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 1.4x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 1.4x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 1.4x + x2 = 0 + 16 1.4x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 1.4x + x2 = 16 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 16 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 16 + 0.49 Combine like terms: 16 + 0.49 = 16.49 0.49 + 1.4x + x2 = 16.49 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 16.49 Calculate the square root of the right side: 4.060788101 Break this problem into two subproblems by setting (x + 0.7) equal to 4.060788101 and -4.060788101.Subproblem 1
x + 0.7 = 4.060788101 Simplifying x + 0.7 = 4.060788101 Reorder the terms: 0.7 + x = 4.060788101 Solving 0.7 + x = 4.060788101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 4.060788101 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 4.060788101 + -0.7 x = 4.060788101 + -0.7 Combine like terms: 4.060788101 + -0.7 = 3.360788101 x = 3.360788101 Simplifying x = 3.360788101Subproblem 2
x + 0.7 = -4.060788101 Simplifying x + 0.7 = -4.060788101 Reorder the terms: 0.7 + x = -4.060788101 Solving 0.7 + x = -4.060788101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -4.060788101 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -4.060788101 + -0.7 x = -4.060788101 + -0.7 Combine like terms: -4.060788101 + -0.7 = -4.760788101 x = -4.760788101 Simplifying x = -4.760788101Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.360788101, -4.760788101}
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