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Simplifying 8x2 + 4x + 38 = 3x2 + 5x + 86x Reorder the terms: 38 + 4x + 8x2 = 3x2 + 5x + 86x Reorder the terms: 38 + 4x + 8x2 = 5x + 86x + 3x2 Combine like terms: 5x + 86x = 91x 38 + 4x + 8x2 = 91x + 3x2 Solving 38 + 4x + 8x2 = 91x + 3x2 Solving for variable 'x'. Reorder the terms: 38 + 4x + -91x + 8x2 + -3x2 = 91x + 3x2 + -91x + -3x2 Combine like terms: 4x + -91x = -87x 38 + -87x + 8x2 + -3x2 = 91x + 3x2 + -91x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 38 + -87x + 5x2 = 91x + 3x2 + -91x + -3x2 Reorder the terms: 38 + -87x + 5x2 = 91x + -91x + 3x2 + -3x2 Combine like terms: 91x + -91x = 0 38 + -87x + 5x2 = 0 + 3x2 + -3x2 38 + -87x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 38 + -87x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7.6 + -17.4x + x2 = 0 Move the constant term to the right: Add '-7.6' to each side of the equation. 7.6 + -17.4x + -7.6 + x2 = 0 + -7.6 Reorder the terms: 7.6 + -7.6 + -17.4x + x2 = 0 + -7.6 Combine like terms: 7.6 + -7.6 = 0.0 0.0 + -17.4x + x2 = 0 + -7.6 -17.4x + x2 = 0 + -7.6 Combine like terms: 0 + -7.6 = -7.6 -17.4x + x2 = -7.6 The x term is -17.4x. Take half its coefficient (-8.7). Square it (75.69) and add it to both sides. Add '75.69' to each side of the equation. -17.4x + 75.69 + x2 = -7.6 + 75.69 Reorder the terms: 75.69 + -17.4x + x2 = -7.6 + 75.69 Combine like terms: -7.6 + 75.69 = 68.09 75.69 + -17.4x + x2 = 68.09 Factor a perfect square on the left side: (x + -8.7)(x + -8.7) = 68.09 Calculate the square root of the right side: 8.251666498 Break this problem into two subproblems by setting (x + -8.7) equal to 8.251666498 and -8.251666498.Subproblem 1
x + -8.7 = 8.251666498 Simplifying x + -8.7 = 8.251666498 Reorder the terms: -8.7 + x = 8.251666498 Solving -8.7 + x = 8.251666498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.7' to each side of the equation. -8.7 + 8.7 + x = 8.251666498 + 8.7 Combine like terms: -8.7 + 8.7 = 0.0 0.0 + x = 8.251666498 + 8.7 x = 8.251666498 + 8.7 Combine like terms: 8.251666498 + 8.7 = 16.951666498 x = 16.951666498 Simplifying x = 16.951666498Subproblem 2
x + -8.7 = -8.251666498 Simplifying x + -8.7 = -8.251666498 Reorder the terms: -8.7 + x = -8.251666498 Solving -8.7 + x = -8.251666498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.7' to each side of the equation. -8.7 + 8.7 + x = -8.251666498 + 8.7 Combine like terms: -8.7 + 8.7 = 0.0 0.0 + x = -8.251666498 + 8.7 x = -8.251666498 + 8.7 Combine like terms: -8.251666498 + 8.7 = 0.448333502 x = 0.448333502 Simplifying x = 0.448333502Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.951666498, 0.448333502}
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