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Simplifying 5x2 + 4x = 196 Reorder the terms: 4x + 5x2 = 196 Solving 4x + 5x2 = 196 Solving for variable 'x'. Reorder the terms: -196 + 4x + 5x2 = 196 + -196 Combine like terms: 196 + -196 = 0 -196 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -39.2 + 0.8x + x2 = 0 Move the constant term to the right: Add '39.2' to each side of the equation. -39.2 + 0.8x + 39.2 + x2 = 0 + 39.2 Reorder the terms: -39.2 + 39.2 + 0.8x + x2 = 0 + 39.2 Combine like terms: -39.2 + 39.2 = 0.0 0.0 + 0.8x + x2 = 0 + 39.2 0.8x + x2 = 0 + 39.2 Combine like terms: 0 + 39.2 = 39.2 0.8x + x2 = 39.2 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 39.2 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 39.2 + 0.16 Combine like terms: 39.2 + 0.16 = 39.36 0.16 + 0.8x + x2 = 39.36 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 39.36 Calculate the square root of the right side: 6.273754857 Break this problem into two subproblems by setting (x + 0.4) equal to 6.273754857 and -6.273754857.Subproblem 1
x + 0.4 = 6.273754857 Simplifying x + 0.4 = 6.273754857 Reorder the terms: 0.4 + x = 6.273754857 Solving 0.4 + x = 6.273754857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 6.273754857 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 6.273754857 + -0.4 x = 6.273754857 + -0.4 Combine like terms: 6.273754857 + -0.4 = 5.873754857 x = 5.873754857 Simplifying x = 5.873754857Subproblem 2
x + 0.4 = -6.273754857 Simplifying x + 0.4 = -6.273754857 Reorder the terms: 0.4 + x = -6.273754857 Solving 0.4 + x = -6.273754857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -6.273754857 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -6.273754857 + -0.4 x = -6.273754857 + -0.4 Combine like terms: -6.273754857 + -0.4 = -6.673754857 x = -6.673754857 Simplifying x = -6.673754857Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.873754857, -6.673754857}
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