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Simplifying 5x2 + 5x = 11 Reorder the terms: 5x + 5x2 = 11 Solving 5x + 5x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 5x + 5x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x + x2 = 0 + 2.2 x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 x + x2 = 2.2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 2.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2.2 + 0.25 Combine like terms: 2.2 + 0.25 = 2.45 1.25 + x2 = 2.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.45 Calculate the square root of the right side: 1.565247584 Break this problem into two subproblems by setting (x + 0.5) equal to 1.565247584 and -1.565247584.Subproblem 1
x + 0.5 = 1.565247584 Simplifying x + 0.5 = 1.565247584 Reorder the terms: 0.5 + x = 1.565247584 Solving 0.5 + x = 1.565247584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.565247584 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.565247584 + -0.5 x = 1.565247584 + -0.5 Combine like terms: 1.565247584 + -0.5 = 1.065247584 x = 1.065247584 Simplifying x = 1.065247584Subproblem 2
x + 0.5 = -1.565247584 Simplifying x + 0.5 = -1.565247584 Reorder the terms: 0.5 + x = -1.565247584 Solving 0.5 + x = -1.565247584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.565247584 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.565247584 + -0.5 x = -1.565247584 + -0.5 Combine like terms: -1.565247584 + -0.5 = -2.065247584 x = -2.065247584 Simplifying x = -2.065247584Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.065247584, -2.065247584}
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