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Simplifying (6x2 + 15x + 3) = 0 Reorder the terms: (3 + 15x + 6x2) = 0 Remove parenthesis around (3 + 15x + 6x2) 3 + 15x + 6x2 = 0 Solving 3 + 15x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 5x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + 5x + 2x2 = 0 Solving 1 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 2.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 2.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 2.5x + x2 = 0 + -0.5 2.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 2.5x + x2 = -0.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -0.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -0.5 + 1.5625 Combine like terms: -0.5 + 1.5625 = 1.0625 1.5625 + 2.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + 1.25) equal to 1.030776406 and -1.030776406.Subproblem 1
x + 1.25 = 1.030776406 Simplifying x + 1.25 = 1.030776406 Reorder the terms: 1.25 + x = 1.030776406 Solving 1.25 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.030776406 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.030776406 + -1.25 x = 1.030776406 + -1.25 Combine like terms: 1.030776406 + -1.25 = -0.219223594 x = -0.219223594 Simplifying x = -0.219223594Subproblem 2
x + 1.25 = -1.030776406 Simplifying x + 1.25 = -1.030776406 Reorder the terms: 1.25 + x = -1.030776406 Solving 1.25 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.030776406 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.030776406 + -1.25 x = -1.030776406 + -1.25 Combine like terms: -1.030776406 + -1.25 = -2.280776406 x = -2.280776406 Simplifying x = -2.280776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.219223594, -2.280776406}Solution
x = {-0.219223594, -2.280776406}
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