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Simplifying 4x2 + 3x = 8(x + 2) Reorder the terms: 3x + 4x2 = 8(x + 2) Reorder the terms: 3x + 4x2 = 8(2 + x) 3x + 4x2 = (2 * 8 + x * 8) 3x + 4x2 = (16 + 8x) Solving 3x + 4x2 = 16 + 8x Solving for variable 'x'. Reorder the terms: -16 + 3x + -8x + 4x2 = 16 + 8x + -16 + -8x Combine like terms: 3x + -8x = -5x -16 + -5x + 4x2 = 16 + 8x + -16 + -8x Reorder the terms: -16 + -5x + 4x2 = 16 + -16 + 8x + -8x Combine like terms: 16 + -16 = 0 -16 + -5x + 4x2 = 0 + 8x + -8x -16 + -5x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -16 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4 + -1.25x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.25x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1.25x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.25x + x2 = 0 + 4 -1.25x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.25x + x2 = 4 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 4 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 4 + 0.390625 Combine like terms: 4 + 0.390625 = 4.390625 0.390625 + -1.25x + x2 = 4.390625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (x + -0.625) equal to 2.095381827 and -2.095381827.Subproblem 1
x + -0.625 = 2.095381827 Simplifying x + -0.625 = 2.095381827 Reorder the terms: -0.625 + x = 2.095381827 Solving -0.625 + x = 2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 2.095381827 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 2.095381827 + 0.625 x = 2.095381827 + 0.625 Combine like terms: 2.095381827 + 0.625 = 2.720381827 x = 2.720381827 Simplifying x = 2.720381827Subproblem 2
x + -0.625 = -2.095381827 Simplifying x + -0.625 = -2.095381827 Reorder the terms: -0.625 + x = -2.095381827 Solving -0.625 + x = -2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -2.095381827 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -2.095381827 + 0.625 x = -2.095381827 + 0.625 Combine like terms: -2.095381827 + 0.625 = -1.470381827 x = -1.470381827 Simplifying x = -1.470381827Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.720381827, -1.470381827}
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