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Simplifying 2x + 10x2 = 255 Solving 2x + 10x2 = 255 Solving for variable 'x'. Reorder the terms: -255 + 2x + 10x2 = 255 + -255 Combine like terms: 255 + -255 = 0 -255 + 2x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -25.5 + 0.2x + x2 = 0 Move the constant term to the right: Add '25.5' to each side of the equation. -25.5 + 0.2x + 25.5 + x2 = 0 + 25.5 Reorder the terms: -25.5 + 25.5 + 0.2x + x2 = 0 + 25.5 Combine like terms: -25.5 + 25.5 = 0.0 0.0 + 0.2x + x2 = 0 + 25.5 0.2x + x2 = 0 + 25.5 Combine like terms: 0 + 25.5 = 25.5 0.2x + x2 = 25.5 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 = 25.5 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 25.5 + 0.01 Combine like terms: 25.5 + 0.01 = 25.51 0.01 + 0.2x + x2 = 25.51 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 25.51 Calculate the square root of the right side: 5.05074252 Break this problem into two subproblems by setting (x + 0.1) equal to 5.05074252 and -5.05074252.Subproblem 1
x + 0.1 = 5.05074252 Simplifying x + 0.1 = 5.05074252 Reorder the terms: 0.1 + x = 5.05074252 Solving 0.1 + x = 5.05074252 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 = 5.05074252 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 5.05074252 + -0.1 x = 5.05074252 + -0.1 Combine like terms: 5.05074252 + -0.1 = 4.95074252 x = 4.95074252 Simplifying x = 4.95074252Subproblem 2
x + 0.1 = -5.05074252 Simplifying x + 0.1 = -5.05074252 Reorder the terms: 0.1 + x = -5.05074252 Solving 0.1 + x = -5.05074252 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 = -5.05074252 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -5.05074252 + -0.1 x = -5.05074252 + -0.1 Combine like terms: -5.05074252 + -0.1 = -5.15074252 x = -5.15074252 Simplifying x = -5.15074252Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.95074252, -5.15074252}
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