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Simplifying 21x2 = 63x + 3 Reorder the terms: 21x2 = 3 + 63x Solving 21x2 = 3 + 63x Solving for variable 'x'. Reorder the terms: -3 + -63x + 21x2 = 3 + 63x + -3 + -63x Reorder the terms: -3 + -63x + 21x2 = 3 + -3 + 63x + -63x Combine like terms: 3 + -3 = 0 -3 + -63x + 21x2 = 0 + 63x + -63x -3 + -63x + 21x2 = 63x + -63x Combine like terms: 63x + -63x = 0 -3 + -63x + 21x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -21x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -21x + 7x2)' equal to zero and attempt to solve: Simplifying -1 + -21x + 7x2 = 0 Solving -1 + -21x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -3x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -3x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -3x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + 0.1428571429 -3x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -3x + x2 = 0.1428571429 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.1428571429 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.1428571429 + 2.25 Combine like terms: 0.1428571429 + 2.25 = 2.3928571429 2.25 + -3x + x2 = 2.3928571429 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.3928571429 Calculate the square root of the right side: 1.546886273 Break this problem into two subproblems by setting (x + -1.5) equal to 1.546886273 and -1.546886273.Subproblem 1
x + -1.5 = 1.546886273 Simplifying x + -1.5 = 1.546886273 Reorder the terms: -1.5 + x = 1.546886273 Solving -1.5 + x = 1.546886273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.546886273 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.546886273 + 1.5 x = 1.546886273 + 1.5 Combine like terms: 1.546886273 + 1.5 = 3.046886273 x = 3.046886273 Simplifying x = 3.046886273Subproblem 2
x + -1.5 = -1.546886273 Simplifying x + -1.5 = -1.546886273 Reorder the terms: -1.5 + x = -1.546886273 Solving -1.5 + x = -1.546886273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.546886273 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.546886273 + 1.5 x = -1.546886273 + 1.5 Combine like terms: -1.546886273 + 1.5 = -0.046886273 x = -0.046886273 Simplifying x = -0.046886273Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.046886273, -0.046886273}Solution
x = {3.046886273, -0.046886273}
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