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Simplifying 5x2 = 5x + 13 Reorder the terms: 5x2 = 13 + 5x Solving 5x2 = 13 + 5x Solving for variable 'x'. Reorder the terms: -13 + -5x + 5x2 = 13 + 5x + -13 + -5x Reorder the terms: -13 + -5x + 5x2 = 13 + -13 + 5x + -5x Combine like terms: 13 + -13 = 0 -13 + -5x + 5x2 = 0 + 5x + -5x -13 + -5x + 5x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -13 + -5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + -1x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -1x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -1x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -1x + x2 = 0 + 2.6 -1x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -1x + x2 = 2.6 The x term is -1x. 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. -1x + 0.25 + x2 = 2.6 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.6 + 0.25 Combine like terms: 2.6 + 0.25 = 2.85 0.25 + -1x + x2 = 2.85 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.85 Calculate the square root of the right side: 1.688194302 Break this problem into two subproblems by setting (x + -0.5) equal to 1.688194302 and -1.688194302.Subproblem 1
x + -0.5 = 1.688194302 Simplifying x + -0.5 = 1.688194302 Reorder the terms: -0.5 + x = 1.688194302 Solving -0.5 + x = 1.688194302 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 = 1.688194302 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.688194302 + 0.5 x = 1.688194302 + 0.5 Combine like terms: 1.688194302 + 0.5 = 2.188194302 x = 2.188194302 Simplifying x = 2.188194302Subproblem 2
x + -0.5 = -1.688194302 Simplifying x + -0.5 = -1.688194302 Reorder the terms: -0.5 + x = -1.688194302 Solving -0.5 + x = -1.688194302 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 = -1.688194302 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.688194302 + 0.5 x = -1.688194302 + 0.5 Combine like terms: -1.688194302 + 0.5 = -1.188194302 x = -1.188194302 Simplifying x = -1.188194302Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.188194302, -1.188194302}
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