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Simplifying 5x2 + -96x + 260 = 0 Reorder the terms: 260 + -96x + 5x2 = 0 Solving 260 + -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'. 52 + -19.2x + x2 = 0 Move the constant term to the right: Add '-52' to each side of the equation. 52 + -19.2x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + -19.2x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -19.2x + x2 = 0 + -52 -19.2x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 -19.2x + x2 = -52 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 = -52 + 92.16 Reorder the terms: 92.16 + -19.2x + x2 = -52 + 92.16 Combine like terms: -52 + 92.16 = 40.16 92.16 + -19.2x + x2 = 40.16 Factor a perfect square on the left side: (x + -9.6)(x + -9.6) = 40.16 Calculate the square root of the right side: 6.337191807 Break this problem into two subproblems by setting (x + -9.6) equal to 6.337191807 and -6.337191807.Subproblem 1
x + -9.6 = 6.337191807 Simplifying x + -9.6 = 6.337191807 Reorder the terms: -9.6 + x = 6.337191807 Solving -9.6 + x = 6.337191807 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 = 6.337191807 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + x = 6.337191807 + 9.6 x = 6.337191807 + 9.6 Combine like terms: 6.337191807 + 9.6 = 15.937191807 x = 15.937191807 Simplifying x = 15.937191807Subproblem 2
x + -9.6 = -6.337191807 Simplifying x + -9.6 = -6.337191807 Reorder the terms: -9.6 + x = -6.337191807 Solving -9.6 + x = -6.337191807 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 = -6.337191807 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + x = -6.337191807 + 9.6 x = -6.337191807 + 9.6 Combine like terms: -6.337191807 + 9.6 = 3.262808193 x = 3.262808193 Simplifying x = 3.262808193Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.937191807, 3.262808193}
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