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Simplifying 4x2 + -5x + 21 = 16x + 28 Reorder the terms: 21 + -5x + 4x2 = 16x + 28 Reorder the terms: 21 + -5x + 4x2 = 28 + 16x Solving 21 + -5x + 4x2 = 28 + 16x Solving for variable 'x'. Reorder the terms: 21 + -28 + -5x + -16x + 4x2 = 28 + 16x + -28 + -16x Combine like terms: 21 + -28 = -7 -7 + -5x + -16x + 4x2 = 28 + 16x + -28 + -16x Combine like terms: -5x + -16x = -21x -7 + -21x + 4x2 = 28 + 16x + -28 + -16x Reorder the terms: -7 + -21x + 4x2 = 28 + -28 + 16x + -16x Combine like terms: 28 + -28 = 0 -7 + -21x + 4x2 = 0 + 16x + -16x -7 + -21x + 4x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -7 + -21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -5.25x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -5.25x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -5.25x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -5.25x + x2 = 0 + 1.75 -5.25x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -5.25x + x2 = 1.75 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = 1.75 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = 1.75 + 6.890625 Combine like terms: 1.75 + 6.890625 = 8.640625 6.890625 + -5.25x + x2 = 8.640625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 8.640625 Calculate the square root of the right side: 2.939494004 Break this problem into two subproblems by setting (x + -2.625) equal to 2.939494004 and -2.939494004.Subproblem 1
x + -2.625 = 2.939494004 Simplifying x + -2.625 = 2.939494004 Reorder the terms: -2.625 + x = 2.939494004 Solving -2.625 + x = 2.939494004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 2.939494004 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 2.939494004 + 2.625 x = 2.939494004 + 2.625 Combine like terms: 2.939494004 + 2.625 = 5.564494004 x = 5.564494004 Simplifying x = 5.564494004Subproblem 2
x + -2.625 = -2.939494004 Simplifying x + -2.625 = -2.939494004 Reorder the terms: -2.625 + x = -2.939494004 Solving -2.625 + x = -2.939494004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -2.939494004 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -2.939494004 + 2.625 x = -2.939494004 + 2.625 Combine like terms: -2.939494004 + 2.625 = -0.314494004 x = -0.314494004 Simplifying x = -0.314494004Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.564494004, -0.314494004}
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