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Simplifying 5x2 + -96x + 80 = 0 Reorder the terms: 80 + -96x + 5x2 = 0 Solving 80 + -96x + 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 + -19.2x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -19.2x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -19.2x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -19.2x + x2 = 0 + -16 -19.2x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -19.2x + x2 = -16 The x term is -19.2x. Take half its coefficient (-9.6). Square it (92.16) and add it to both sides. Add '92.16' to each side of the equation. -19.2x + 92.16 + x2 = -16 + 92.16 Reorder the terms: 92.16 + -19.2x + x2 = -16 + 92.16 Combine like terms: -16 + 92.16 = 76.16 92.16 + -19.2x + x2 = 76.16 Factor a perfect square on the left side: (x + -9.6)(x + -9.6) = 76.16 Calculate the square root of the right side: 8.726969692 Break this problem into two subproblems by setting (x + -9.6) equal to 8.726969692 and -8.726969692.Subproblem 1
x + -9.6 = 8.726969692 Simplifying x + -9.6 = 8.726969692 Reorder the terms: -9.6 + x = 8.726969692 Solving -9.6 + x = 8.726969692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.6' to each side of the equation. -9.6 + 9.6 + x = 8.726969692 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + x = 8.726969692 + 9.6 x = 8.726969692 + 9.6 Combine like terms: 8.726969692 + 9.6 = 18.326969692 x = 18.326969692 Simplifying x = 18.326969692Subproblem 2
x + -9.6 = -8.726969692 Simplifying x + -9.6 = -8.726969692 Reorder the terms: -9.6 + x = -8.726969692 Solving -9.6 + x = -8.726969692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.6' to each side of the equation. -9.6 + 9.6 + x = -8.726969692 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + x = -8.726969692 + 9.6 x = -8.726969692 + 9.6 Combine like terms: -8.726969692 + 9.6 = 0.873030308 x = 0.873030308 Simplifying x = 0.873030308Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.326969692, 0.873030308}
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