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Simplifying 25x2 + 5x = 7 Reorder the terms: 5x + 25x2 = 7 Solving 5x + 25x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 5x + 25x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 5x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.28 + 0.2x + x2 = 0 Move the constant term to the right: Add '0.28' to each side of the equation. -0.28 + 0.2x + 0.28 + x2 = 0 + 0.28 Reorder the terms: -0.28 + 0.28 + 0.2x + x2 = 0 + 0.28 Combine like terms: -0.28 + 0.28 = 0.00 0.00 + 0.2x + x2 = 0 + 0.28 0.2x + x2 = 0 + 0.28 Combine like terms: 0 + 0.28 = 0.28 0.2x + x2 = 0.28 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 = 0.28 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.28 + 0.01 Combine like terms: 0.28 + 0.01 = 0.29 0.01 + 0.2x + x2 = 0.29 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (x + 0.1) equal to 0.538516481 and -0.538516481.Subproblem 1
x + 0.1 = 0.538516481 Simplifying x + 0.1 = 0.538516481 Reorder the terms: 0.1 + x = 0.538516481 Solving 0.1 + x = 0.538516481 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 = 0.538516481 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.538516481 + -0.1 x = 0.538516481 + -0.1 Combine like terms: 0.538516481 + -0.1 = 0.438516481 x = 0.438516481 Simplifying x = 0.438516481Subproblem 2
x + 0.1 = -0.538516481 Simplifying x + 0.1 = -0.538516481 Reorder the terms: 0.1 + x = -0.538516481 Solving 0.1 + x = -0.538516481 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 = -0.538516481 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.538516481 + -0.1 x = -0.538516481 + -0.1 Combine like terms: -0.538516481 + -0.1 = -0.638516481 x = -0.638516481 Simplifying x = -0.638516481Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.438516481, -0.638516481}
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