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Simplifying 4x2 + -29x + 24 = 8x + 4 Reorder the terms: 24 + -29x + 4x2 = 8x + 4 Reorder the terms: 24 + -29x + 4x2 = 4 + 8x Solving 24 + -29x + 4x2 = 4 + 8x Solving for variable 'x'. Reorder the terms: 24 + -4 + -29x + -8x + 4x2 = 4 + 8x + -4 + -8x Combine like terms: 24 + -4 = 20 20 + -29x + -8x + 4x2 = 4 + 8x + -4 + -8x Combine like terms: -29x + -8x = -37x 20 + -37x + 4x2 = 4 + 8x + -4 + -8x Reorder the terms: 20 + -37x + 4x2 = 4 + -4 + 8x + -8x Combine like terms: 4 + -4 = 0 20 + -37x + 4x2 = 0 + 8x + -8x 20 + -37x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 20 + -37x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5 + -9.25x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -9.25x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -9.25x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9.25x + x2 = 0 + -5 -9.25x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -9.25x + x2 = -5 The x term is -9.25x. Take half its coefficient (-4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. -9.25x + 21.390625 + x2 = -5 + 21.390625 Reorder the terms: 21.390625 + -9.25x + x2 = -5 + 21.390625 Combine like terms: -5 + 21.390625 = 16.390625 21.390625 + -9.25x + x2 = 16.390625 Factor a perfect square on the left side: (x + -4.625)(x + -4.625) = 16.390625 Calculate the square root of the right side: 4.048533685 Break this problem into two subproblems by setting (x + -4.625) equal to 4.048533685 and -4.048533685.Subproblem 1
x + -4.625 = 4.048533685 Simplifying x + -4.625 = 4.048533685 Reorder the terms: -4.625 + x = 4.048533685 Solving -4.625 + x = 4.048533685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + x = 4.048533685 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = 4.048533685 + 4.625 x = 4.048533685 + 4.625 Combine like terms: 4.048533685 + 4.625 = 8.673533685 x = 8.673533685 Simplifying x = 8.673533685Subproblem 2
x + -4.625 = -4.048533685 Simplifying x + -4.625 = -4.048533685 Reorder the terms: -4.625 + x = -4.048533685 Solving -4.625 + x = -4.048533685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + x = -4.048533685 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = -4.048533685 + 4.625 x = -4.048533685 + 4.625 Combine like terms: -4.048533685 + 4.625 = 0.576466315 x = 0.576466315 Simplifying x = 0.576466315Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.673533685, 0.576466315}
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