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Simplifying 5x2 + -22x + -80 = 0 Reorder the terms: -80 + -22x + 5x2 = 0 Solving -80 + -22x + 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 + -4.4x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -4.4x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -4.4x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -4.4x + x2 = 0 + 16 -4.4x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -4.4x + x2 = 16 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = 16 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = 16 + 4.84 Combine like terms: 16 + 4.84 = 20.84 4.84 + -4.4x + x2 = 20.84 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 20.84 Calculate the square root of the right side: 4.565084884 Break this problem into two subproblems by setting (x + -2.2) equal to 4.565084884 and -4.565084884.Subproblem 1
x + -2.2 = 4.565084884 Simplifying x + -2.2 = 4.565084884 Reorder the terms: -2.2 + x = 4.565084884 Solving -2.2 + x = 4.565084884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 4.565084884 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 4.565084884 + 2.2 x = 4.565084884 + 2.2 Combine like terms: 4.565084884 + 2.2 = 6.765084884 x = 6.765084884 Simplifying x = 6.765084884Subproblem 2
x + -2.2 = -4.565084884 Simplifying x + -2.2 = -4.565084884 Reorder the terms: -2.2 + x = -4.565084884 Solving -2.2 + x = -4.565084884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -4.565084884 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -4.565084884 + 2.2 x = -4.565084884 + 2.2 Combine like terms: -4.565084884 + 2.2 = -2.365084884 x = -2.365084884 Simplifying x = -2.365084884Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.765084884, -2.365084884}
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