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Simplifying 21x + 3x2 = 21 + 4x Solving 21x + 3x2 = 21 + 4x Solving for variable 'x'. Reorder the terms: -21 + 21x + -4x + 3x2 = 21 + 4x + -21 + -4x Combine like terms: 21x + -4x = 17x -21 + 17x + 3x2 = 21 + 4x + -21 + -4x Reorder the terms: -21 + 17x + 3x2 = 21 + -21 + 4x + -4x Combine like terms: 21 + -21 = 0 -21 + 17x + 3x2 = 0 + 4x + -4x -21 + 17x + 3x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -21 + 17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 5.666666667x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 5.666666667x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5.666666667x + x2 = 0 + 7 5.666666667x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 5.666666667x + x2 = 7 The x term is 5.666666667x. Take half its coefficient (2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. 5.666666667x + 8.027777782 + x2 = 7 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 7 + 8.027777782 Combine like terms: 7 + 8.027777782 = 15.027777782 8.027777782 + 5.666666667x + x2 = 15.027777782 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 15.027777782 Calculate the square root of the right side: 3.876567784 Break this problem into two subproblems by setting (x + 2.833333334) equal to 3.876567784 and -3.876567784.Subproblem 1
x + 2.833333334 = 3.876567784 Simplifying x + 2.833333334 = 3.876567784 Reorder the terms: 2.833333334 + x = 3.876567784 Solving 2.833333334 + x = 3.876567784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = 3.876567784 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 3.876567784 + -2.833333334 x = 3.876567784 + -2.833333334 Combine like terms: 3.876567784 + -2.833333334 = 1.04323445 x = 1.04323445 Simplifying x = 1.04323445Subproblem 2
x + 2.833333334 = -3.876567784 Simplifying x + 2.833333334 = -3.876567784 Reorder the terms: 2.833333334 + x = -3.876567784 Solving 2.833333334 + x = -3.876567784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = -3.876567784 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -3.876567784 + -2.833333334 x = -3.876567784 + -2.833333334 Combine like terms: -3.876567784 + -2.833333334 = -6.709901118 x = -6.709901118 Simplifying x = -6.709901118Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.04323445, -6.709901118}
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