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Simplifying 0 = 15x2 + 105x + 10 Reorder the terms: 0 = 10 + 105x + 15x2 Solving 0 = 10 + 105x + 15x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -105x + -15x2 = 10 + 105x + 15x2 + -10 + -105x + -15x2 Reorder the terms: -10 + -105x + -15x2 = 10 + -10 + 105x + -105x + 15x2 + -15x2 Combine like terms: 10 + -10 = 0 -10 + -105x + -15x2 = 0 + 105x + -105x + 15x2 + -15x2 -10 + -105x + -15x2 = 105x + -105x + 15x2 + -15x2 Combine like terms: 105x + -105x = 0 -10 + -105x + -15x2 = 0 + 15x2 + -15x2 -10 + -105x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -10 + -105x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '-5'. -5(2 + 21x + 3x2) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(2 + 21x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + 21x + 3x2 = 0 Solving 2 + 21x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 7x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 7x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 7x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 7x + x2 = 0 + -0.6666666667 7x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 7x + x2 = -0.6666666667 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -0.6666666667 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -0.6666666667 + 12.25 Combine like terms: -0.6666666667 + 12.25 = 11.5833333333 12.25 + 7x + x2 = 11.5833333333 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 11.5833333333 Calculate the square root of the right side: 3.403429643 Break this problem into two subproblems by setting (x + 3.5) equal to 3.403429643 and -3.403429643.Subproblem 1
x + 3.5 = 3.403429643 Simplifying x + 3.5 = 3.403429643 Reorder the terms: 3.5 + x = 3.403429643 Solving 3.5 + x = 3.403429643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.403429643 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.403429643 + -3.5 x = 3.403429643 + -3.5 Combine like terms: 3.403429643 + -3.5 = -0.096570357 x = -0.096570357 Simplifying x = -0.096570357Subproblem 2
x + 3.5 = -3.403429643 Simplifying x + 3.5 = -3.403429643 Reorder the terms: 3.5 + x = -3.403429643 Solving 3.5 + x = -3.403429643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.403429643 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.403429643 + -3.5 x = -3.403429643 + -3.5 Combine like terms: -3.403429643 + -3.5 = -6.903429643 x = -6.903429643 Simplifying x = -6.903429643Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.096570357, -6.903429643}Solution
x = {-0.096570357, -6.903429643}
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