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Simplifying 6x2 + 21x = 114 Reorder the terms: 21x + 6x2 = 114 Solving 21x + 6x2 = 114 Solving for variable 'x'. Reorder the terms: -114 + 21x + 6x2 = 114 + -114 Combine like terms: 114 + -114 = 0 -114 + 21x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-38 + 7x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-38 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying -38 + 7x + 2x2 = 0 Solving -38 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19 + 3.5x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 3.5x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 3.5x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 3.5x + x2 = 0 + 19 3.5x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 3.5x + x2 = 19 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 19 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 19 + 3.0625 Combine like terms: 19 + 3.0625 = 22.0625 3.0625 + 3.5x + x2 = 22.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (x + 1.75) equal to 4.697073557 and -4.697073557.Subproblem 1
x + 1.75 = 4.697073557 Simplifying x + 1.75 = 4.697073557 Reorder the terms: 1.75 + x = 4.697073557 Solving 1.75 + x = 4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 4.697073557 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.697073557 + -1.75 x = 4.697073557 + -1.75 Combine like terms: 4.697073557 + -1.75 = 2.947073557 x = 2.947073557 Simplifying x = 2.947073557Subproblem 2
x + 1.75 = -4.697073557 Simplifying x + 1.75 = -4.697073557 Reorder the terms: 1.75 + x = -4.697073557 Solving 1.75 + x = -4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -4.697073557 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.697073557 + -1.75 x = -4.697073557 + -1.75 Combine like terms: -4.697073557 + -1.75 = -6.447073557 x = -6.447073557 Simplifying x = -6.447073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.947073557, -6.447073557}Solution
x = {2.947073557, -6.447073557}
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