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Simplifying 2x(5x + 1) + -11 = 0 Reorder the terms: 2x(1 + 5x) + -11 = 0 (1 * 2x + 5x * 2x) + -11 = 0 (2x + 10x2) + -11 = 0 Reorder the terms: -11 + 2x + 10x2 = 0 Solving -11 + 2x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.1 + 0.2x + x2 = 0.0 Move the constant term to the right: Add '1.1' to each side of the equation. -1.1 + 0.2x + 1.1 + x2 = 0.0 + 1.1 Reorder the terms: -1.1 + 1.1 + 0.2x + x2 = 0.0 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + 0.2x + x2 = 0.0 + 1.1 0.2x + x2 = 0.0 + 1.1 Combine like terms: 0.0 + 1.1 = 1.1 0.2x + x2 = 1.1 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 = 1.1 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 1.1 + 0.01 Combine like terms: 1.1 + 0.01 = 1.11 0.01 + 0.2x + x2 = 1.11 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 1.11 Calculate the square root of the right side: 1.053565375 Break this problem into two subproblems by setting (x + 0.1) equal to 1.053565375 and -1.053565375.Subproblem 1
x + 0.1 = 1.053565375 Simplifying x + 0.1 = 1.053565375 Reorder the terms: 0.1 + x = 1.053565375 Solving 0.1 + x = 1.053565375 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 = 1.053565375 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.053565375 + -0.1 x = 1.053565375 + -0.1 Combine like terms: 1.053565375 + -0.1 = 0.953565375 x = 0.953565375 Simplifying x = 0.953565375Subproblem 2
x + 0.1 = -1.053565375 Simplifying x + 0.1 = -1.053565375 Reorder the terms: 0.1 + x = -1.053565375 Solving 0.1 + x = -1.053565375 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 = -1.053565375 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.053565375 + -0.1 x = -1.053565375 + -0.1 Combine like terms: -1.053565375 + -0.1 = -1.153565375 x = -1.153565375 Simplifying x = -1.153565375Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.953565375, -1.153565375}
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