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Simplifying 0 = 5x2 + -28x + -80 Reorder the terms: 0 = -80 + -28x + 5x2 Solving 0 = -80 + -28x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 80 = 80 80 + 28x + -5x2 = -80 + -28x + 5x2 + 80 + 28x + -5x2 Reorder the terms: 80 + 28x + -5x2 = -80 + 80 + -28x + 28x + 5x2 + -5x2 Combine like terms: -80 + 80 = 0 80 + 28x + -5x2 = 0 + -28x + 28x + 5x2 + -5x2 80 + 28x + -5x2 = -28x + 28x + 5x2 + -5x2 Combine like terms: -28x + 28x = 0 80 + 28x + -5x2 = 0 + 5x2 + -5x2 80 + 28x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 80 + 28x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -16 + -5.6x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -5.6x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -5.6x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -5.6x + x2 = 0 + 16 -5.6x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -5.6x + x2 = 16 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = 16 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = 16 + 7.84 Combine like terms: 16 + 7.84 = 23.84 7.84 + -5.6x + x2 = 23.84 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 23.84 Calculate the square root of the right side: 4.882622246 Break this problem into two subproblems by setting (x + -2.8) equal to 4.882622246 and -4.882622246.Subproblem 1
x + -2.8 = 4.882622246 Simplifying x + -2.8 = 4.882622246 Reorder the terms: -2.8 + x = 4.882622246 Solving -2.8 + x = 4.882622246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 4.882622246 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 4.882622246 + 2.8 x = 4.882622246 + 2.8 Combine like terms: 4.882622246 + 2.8 = 7.682622246 x = 7.682622246 Simplifying x = 7.682622246Subproblem 2
x + -2.8 = -4.882622246 Simplifying x + -2.8 = -4.882622246 Reorder the terms: -2.8 + x = -4.882622246 Solving -2.8 + x = -4.882622246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -4.882622246 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -4.882622246 + 2.8 x = -4.882622246 + 2.8 Combine like terms: -4.882622246 + 2.8 = -2.082622246 x = -2.082622246 Simplifying x = -2.082622246Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.682622246, -2.082622246}
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