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Simplifying 5x2 = 34 + (8x + 38) Reorder the terms: 5x2 = 34 + (38 + 8x) Remove parenthesis around (38 + 8x) 5x2 = 34 + 38 + 8x Combine like terms: 34 + 38 = 72 5x2 = 72 + 8x Solving 5x2 = 72 + 8x Solving for variable 'x'. Reorder the terms: -72 + -8x + 5x2 = 72 + 8x + -72 + -8x Reorder the terms: -72 + -8x + 5x2 = 72 + -72 + 8x + -8x Combine like terms: 72 + -72 = 0 -72 + -8x + 5x2 = 0 + 8x + -8x -72 + -8x + 5x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -72 + -8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14.4 + -1.6x + x2 = 0 Move the constant term to the right: Add '14.4' to each side of the equation. -14.4 + -1.6x + 14.4 + x2 = 0 + 14.4 Reorder the terms: -14.4 + 14.4 + -1.6x + x2 = 0 + 14.4 Combine like terms: -14.4 + 14.4 = 0.0 0.0 + -1.6x + x2 = 0 + 14.4 -1.6x + x2 = 0 + 14.4 Combine like terms: 0 + 14.4 = 14.4 -1.6x + x2 = 14.4 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 = 14.4 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 14.4 + 0.64 Combine like terms: 14.4 + 0.64 = 15.04 0.64 + -1.6x + x2 = 15.04 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 15.04 Calculate the square root of the right side: 3.878143886 Break this problem into two subproblems by setting (x + -0.8) equal to 3.878143886 and -3.878143886.Subproblem 1
x + -0.8 = 3.878143886 Simplifying x + -0.8 = 3.878143886 Reorder the terms: -0.8 + x = 3.878143886 Solving -0.8 + x = 3.878143886 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 = 3.878143886 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 3.878143886 + 0.8 x = 3.878143886 + 0.8 Combine like terms: 3.878143886 + 0.8 = 4.678143886 x = 4.678143886 Simplifying x = 4.678143886Subproblem 2
x + -0.8 = -3.878143886 Simplifying x + -0.8 = -3.878143886 Reorder the terms: -0.8 + x = -3.878143886 Solving -0.8 + x = -3.878143886 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 = -3.878143886 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -3.878143886 + 0.8 x = -3.878143886 + 0.8 Combine like terms: -3.878143886 + 0.8 = -3.078143886 x = -3.078143886 Simplifying x = -3.078143886Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.678143886, -3.078143886}
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