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Simplifying 5x2 = 5 + 8x Solving 5x2 = 5 + 8x Solving for variable 'x'. Reorder the terms: -5 + -8x + 5x2 = 5 + 8x + -5 + -8x Reorder the terms: -5 + -8x + 5x2 = 5 + -5 + 8x + -8x Combine like terms: 5 + -5 = 0 -5 + -8x + 5x2 = 0 + 8x + -8x -5 + -8x + 5x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -5 + -8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -1.6x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.6x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.6x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.6x + x2 = 0 + 1 -1.6x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.6x + x2 = 1 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 1 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 1 + 0.64 Combine like terms: 1 + 0.64 = 1.64 0.64 + -1.6x + x2 = 1.64 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 1.64 Calculate the square root of the right side: 1.280624847 Break this problem into two subproblems by setting (x + -0.8) equal to 1.280624847 and -1.280624847.Subproblem 1
x + -0.8 = 1.280624847 Simplifying x + -0.8 = 1.280624847 Reorder the terms: -0.8 + x = 1.280624847 Solving -0.8 + x = 1.280624847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.280624847 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.280624847 + 0.8 x = 1.280624847 + 0.8 Combine like terms: 1.280624847 + 0.8 = 2.080624847 x = 2.080624847 Simplifying x = 2.080624847Subproblem 2
x + -0.8 = -1.280624847 Simplifying x + -0.8 = -1.280624847 Reorder the terms: -0.8 + x = -1.280624847 Solving -0.8 + x = -1.280624847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.280624847 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.280624847 + 0.8 x = -1.280624847 + 0.8 Combine like terms: -1.280624847 + 0.8 = -0.480624847 x = -0.480624847 Simplifying x = -0.480624847Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.080624847, -0.480624847}
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