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Simplifying 2x(5x + 3) = 11 Reorder the terms: 2x(3 + 5x) = 11 (3 * 2x + 5x * 2x) = 11 (6x + 10x2) = 11 Solving 6x + 10x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 6x + 10x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 6x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.1 + 0.6x + x2 = 0.0 Move the constant term to the right: Add '1.1' to each side of the equation. -1.1 + 0.6x + 1.1 + x2 = 0.0 + 1.1 Reorder the terms: -1.1 + 1.1 + 0.6x + x2 = 0.0 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + 0.6x + x2 = 0.0 + 1.1 0.6x + x2 = 0.0 + 1.1 Combine like terms: 0.0 + 1.1 = 1.1 0.6x + x2 = 1.1 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 1.1 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 1.1 + 0.09 Combine like terms: 1.1 + 0.09 = 1.19 0.09 + 0.6x + x2 = 1.19 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 1.19 Calculate the square root of the right side: 1.090871211 Break this problem into two subproblems by setting (x + 0.3) equal to 1.090871211 and -1.090871211.Subproblem 1
x + 0.3 = 1.090871211 Simplifying x + 0.3 = 1.090871211 Reorder the terms: 0.3 + x = 1.090871211 Solving 0.3 + x = 1.090871211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 1.090871211 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.090871211 + -0.3 x = 1.090871211 + -0.3 Combine like terms: 1.090871211 + -0.3 = 0.790871211 x = 0.790871211 Simplifying x = 0.790871211Subproblem 2
x + 0.3 = -1.090871211 Simplifying x + 0.3 = -1.090871211 Reorder the terms: 0.3 + x = -1.090871211 Solving 0.3 + x = -1.090871211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -1.090871211 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.090871211 + -0.3 x = -1.090871211 + -0.3 Combine like terms: -1.090871211 + -0.3 = -1.390871211 x = -1.390871211 Simplifying x = -1.390871211Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.790871211, -1.390871211}
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