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Simplifying 5(x + 5) * x = 6 Reorder the terms: 5(5 + x) * x = 6 Reorder the terms for easier multiplication: 5x(5 + x) = 6 (5 * 5x + x * 5x) = 6 (25x + 5x2) = 6 Solving 25x + 5x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 25x + 5x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 25x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 5x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 5x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 5x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 5x + x2 = 0 + 1.2 5x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 5x + x2 = 1.2 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 1.2 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1.2 + 6.25 Combine like terms: 1.2 + 6.25 = 7.45 6.25 + 5x + x2 = 7.45 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 7.45 Calculate the square root of the right side: 2.729468813 Break this problem into two subproblems by setting (x + 2.5) equal to 2.729468813 and -2.729468813.Subproblem 1
x + 2.5 = 2.729468813 Simplifying x + 2.5 = 2.729468813 Reorder the terms: 2.5 + x = 2.729468813 Solving 2.5 + x = 2.729468813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.729468813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.729468813 + -2.5 x = 2.729468813 + -2.5 Combine like terms: 2.729468813 + -2.5 = 0.229468813 x = 0.229468813 Simplifying x = 0.229468813Subproblem 2
x + 2.5 = -2.729468813 Simplifying x + 2.5 = -2.729468813 Reorder the terms: 2.5 + x = -2.729468813 Solving 2.5 + x = -2.729468813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.729468813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.729468813 + -2.5 x = -2.729468813 + -2.5 Combine like terms: -2.729468813 + -2.5 = -5.229468813 x = -5.229468813 Simplifying x = -5.229468813Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.229468813, -5.229468813}
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