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Simplifying 2x(4x + 2) = 7x + 21 Reorder the terms: 2x(2 + 4x) = 7x + 21 (2 * 2x + 4x * 2x) = 7x + 21 (4x + 8x2) = 7x + 21 Reorder the terms: 4x + 8x2 = 21 + 7x Solving 4x + 8x2 = 21 + 7x Solving for variable 'x'. Reorder the terms: -21 + 4x + -7x + 8x2 = 21 + 7x + -21 + -7x Combine like terms: 4x + -7x = -3x -21 + -3x + 8x2 = 21 + 7x + -21 + -7x Reorder the terms: -21 + -3x + 8x2 = 21 + -21 + 7x + -7x Combine like terms: 21 + -21 = 0 -21 + -3x + 8x2 = 0 + 7x + -7x -21 + -3x + 8x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -21 + -3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.625 + -0.375x + x2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + -0.375x + 2.625 + x2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + -0.375x + x2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + -0.375x + x2 = 0 + 2.625 -0.375x + x2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 -0.375x + x2 = 2.625 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 2.625 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 2.625 + 0.03515625 Combine like terms: 2.625 + 0.03515625 = 2.66015625 0.03515625 + -0.375x + x2 = 2.66015625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 2.66015625 Calculate the square root of the right side: 1.630998544 Break this problem into two subproblems by setting (x + -0.1875) equal to 1.630998544 and -1.630998544.Subproblem 1
x + -0.1875 = 1.630998544 Simplifying x + -0.1875 = 1.630998544 Reorder the terms: -0.1875 + x = 1.630998544 Solving -0.1875 + x = 1.630998544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 1.630998544 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 1.630998544 + 0.1875 x = 1.630998544 + 0.1875 Combine like terms: 1.630998544 + 0.1875 = 1.818498544 x = 1.818498544 Simplifying x = 1.818498544Subproblem 2
x + -0.1875 = -1.630998544 Simplifying x + -0.1875 = -1.630998544 Reorder the terms: -0.1875 + x = -1.630998544 Solving -0.1875 + x = -1.630998544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -1.630998544 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -1.630998544 + 0.1875 x = -1.630998544 + 0.1875 Combine like terms: -1.630998544 + 0.1875 = -1.443498544 x = -1.443498544 Simplifying x = -1.443498544Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.818498544, -1.443498544}
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