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Simplifying 5x2 = 38x + 56 Reorder the terms: 5x2 = 56 + 38x Solving 5x2 = 56 + 38x Solving for variable 'x'. Reorder the terms: -56 + -38x + 5x2 = 56 + 38x + -56 + -38x Reorder the terms: -56 + -38x + 5x2 = 56 + -56 + 38x + -38x Combine like terms: 56 + -56 = 0 -56 + -38x + 5x2 = 0 + 38x + -38x -56 + -38x + 5x2 = 38x + -38x Combine like terms: 38x + -38x = 0 -56 + -38x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -11.2 + -7.6x + x2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + -7.6x + 11.2 + x2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + -7.6x + x2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + -7.6x + x2 = 0 + 11.2 -7.6x + x2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 -7.6x + x2 = 11.2 The x term is -7.6x. Take half its coefficient (-3.8). Square it (14.44) and add it to both sides. Add '14.44' to each side of the equation. -7.6x + 14.44 + x2 = 11.2 + 14.44 Reorder the terms: 14.44 + -7.6x + x2 = 11.2 + 14.44 Combine like terms: 11.2 + 14.44 = 25.64 14.44 + -7.6x + x2 = 25.64 Factor a perfect square on the left side: (x + -3.8)(x + -3.8) = 25.64 Calculate the square root of the right side: 5.06359556 Break this problem into two subproblems by setting (x + -3.8) equal to 5.06359556 and -5.06359556.Subproblem 1
x + -3.8 = 5.06359556 Simplifying x + -3.8 = 5.06359556 Reorder the terms: -3.8 + x = 5.06359556 Solving -3.8 + x = 5.06359556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = 5.06359556 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = 5.06359556 + 3.8 x = 5.06359556 + 3.8 Combine like terms: 5.06359556 + 3.8 = 8.86359556 x = 8.86359556 Simplifying x = 8.86359556Subproblem 2
x + -3.8 = -5.06359556 Simplifying x + -3.8 = -5.06359556 Reorder the terms: -3.8 + x = -5.06359556 Solving -3.8 + x = -5.06359556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = -5.06359556 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = -5.06359556 + 3.8 x = -5.06359556 + 3.8 Combine like terms: -5.06359556 + 3.8 = -1.26359556 x = -1.26359556 Simplifying x = -1.26359556Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.86359556, -1.26359556}
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