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Simplifying 26x + 5x2 = 492 Solving 26x + 5x2 = 492 Solving for variable 'x'. Reorder the terms: -492 + 26x + 5x2 = 492 + -492 Combine like terms: 492 + -492 = 0 -492 + 26x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -98.4 + 5.2x + x2 = 0 Move the constant term to the right: Add '98.4' to each side of the equation. -98.4 + 5.2x + 98.4 + x2 = 0 + 98.4 Reorder the terms: -98.4 + 98.4 + 5.2x + x2 = 0 + 98.4 Combine like terms: -98.4 + 98.4 = 0.0 0.0 + 5.2x + x2 = 0 + 98.4 5.2x + x2 = 0 + 98.4 Combine like terms: 0 + 98.4 = 98.4 5.2x + x2 = 98.4 The x term is 5.2x. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2x + 6.76 + x2 = 98.4 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = 98.4 + 6.76 Combine like terms: 98.4 + 6.76 = 105.16 6.76 + 5.2x + x2 = 105.16 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 105.16 Calculate the square root of the right side: 10.254754995 Break this problem into two subproblems by setting (x + 2.6) equal to 10.254754995 and -10.254754995.Subproblem 1
x + 2.6 = 10.254754995 Simplifying x + 2.6 = 10.254754995 Reorder the terms: 2.6 + x = 10.254754995 Solving 2.6 + x = 10.254754995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = 10.254754995 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 10.254754995 + -2.6 x = 10.254754995 + -2.6 Combine like terms: 10.254754995 + -2.6 = 7.654754995 x = 7.654754995 Simplifying x = 7.654754995Subproblem 2
x + 2.6 = -10.254754995 Simplifying x + 2.6 = -10.254754995 Reorder the terms: 2.6 + x = -10.254754995 Solving 2.6 + x = -10.254754995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = -10.254754995 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -10.254754995 + -2.6 x = -10.254754995 + -2.6 Combine like terms: -10.254754995 + -2.6 = -12.854754995 x = -12.854754995 Simplifying x = -12.854754995Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.654754995, -12.854754995}
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