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Simplifying 2x(5x + 1) = 7 Reorder the terms: 2x(1 + 5x) = 7 (1 * 2x + 5x * 2x) = 7 (2x + 10x2) = 7 Solving 2x + 10x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 2x + 10x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 2x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.7 + 0.2x + x2 = 0.0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + 0.2x + 0.7 + x2 = 0.0 + 0.7 Reorder the terms: -0.7 + 0.7 + 0.2x + x2 = 0.0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + 0.2x + x2 = 0.0 + 0.7 0.2x + x2 = 0.0 + 0.7 Combine like terms: 0.0 + 0.7 = 0.7 0.2x + x2 = 0.7 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 = 0.7 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.7 + 0.01 Combine like terms: 0.7 + 0.01 = 0.71 0.01 + 0.2x + x2 = 0.71 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.71 Calculate the square root of the right side: 0.842614977 Break this problem into two subproblems by setting (x + 0.1) equal to 0.842614977 and -0.842614977.Subproblem 1
x + 0.1 = 0.842614977 Simplifying x + 0.1 = 0.842614977 Reorder the terms: 0.1 + x = 0.842614977 Solving 0.1 + x = 0.842614977 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 = 0.842614977 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.842614977 + -0.1 x = 0.842614977 + -0.1 Combine like terms: 0.842614977 + -0.1 = 0.742614977 x = 0.742614977 Simplifying x = 0.742614977Subproblem 2
x + 0.1 = -0.842614977 Simplifying x + 0.1 = -0.842614977 Reorder the terms: 0.1 + x = -0.842614977 Solving 0.1 + x = -0.842614977 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 = -0.842614977 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.842614977 + -0.1 x = -0.842614977 + -0.1 Combine like terms: -0.842614977 + -0.1 = -0.942614977 x = -0.942614977 Simplifying x = -0.942614977Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.742614977, -0.942614977}
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