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Simplifying 2x(5x + -1) = 11 Reorder the terms: 2x(-1 + 5x) = 11 (-1 * 2x + 5x * 2x) = 11 (-2x + 10x2) = 11 Solving -2x + 10x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -2x + 10x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -2x + 10x2 = 0 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 = 1.153565375 x = 1.153565375 Simplifying x = 1.153565375Subproblem 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 = -0.953565375 x = -0.953565375 Simplifying x = -0.953565375Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.153565375, -0.953565375}
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