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Simplifying 5x = 11 + -25x2 + 15 Reorder the terms: 5x = 11 + 15 + -25x2 Combine like terms: 11 + 15 = 26 5x = 26 + -25x2 Solving 5x = 26 + -25x2 Solving for variable 'x'. Reorder the terms: -26 + 5x + 25x2 = 26 + -25x2 + -26 + 25x2 Reorder the terms: -26 + 5x + 25x2 = 26 + -26 + -25x2 + 25x2 Combine like terms: 26 + -26 = 0 -26 + 5x + 25x2 = 0 + -25x2 + 25x2 -26 + 5x + 25x2 = -25x2 + 25x2 Combine like terms: -25x2 + 25x2 = 0 -26 + 5x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.04 + 0.2x + x2 = 0 Move the constant term to the right: Add '1.04' to each side of the equation. -1.04 + 0.2x + 1.04 + x2 = 0 + 1.04 Reorder the terms: -1.04 + 1.04 + 0.2x + x2 = 0 + 1.04 Combine like terms: -1.04 + 1.04 = 0.00 0.00 + 0.2x + x2 = 0 + 1.04 0.2x + x2 = 0 + 1.04 Combine like terms: 0 + 1.04 = 1.04 0.2x + x2 = 1.04 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 1.04 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 1.04 + 0.01 Combine like terms: 1.04 + 0.01 = 1.05 0.01 + 0.2x + x2 = 1.05 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 1.05 Calculate the square root of the right side: 1.024695077 Break this problem into two subproblems by setting (x + 0.1) equal to 1.024695077 and -1.024695077.Subproblem 1
x + 0.1 = 1.024695077 Simplifying x + 0.1 = 1.024695077 Reorder the terms: 0.1 + x = 1.024695077 Solving 0.1 + x = 1.024695077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 1.024695077 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.024695077 + -0.1 x = 1.024695077 + -0.1 Combine like terms: 1.024695077 + -0.1 = 0.924695077 x = 0.924695077 Simplifying x = 0.924695077Subproblem 2
x + 0.1 = -1.024695077 Simplifying x + 0.1 = -1.024695077 Reorder the terms: 0.1 + x = -1.024695077 Solving 0.1 + x = -1.024695077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -1.024695077 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.024695077 + -0.1 x = -1.024695077 + -0.1 Combine like terms: -1.024695077 + -0.1 = -1.124695077 x = -1.124695077 Simplifying x = -1.124695077Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.924695077, -1.124695077}
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