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Simplifying 0 = 15x2 + 15x + -168 Reorder the terms: 0 = -168 + 15x + 15x2 Solving 0 = -168 + 15x + 15x2 Solving for variable 'x'. Combine like terms: 0 + 168 = 168 168 + -15x + -15x2 = -168 + 15x + 15x2 + 168 + -15x + -15x2 Reorder the terms: 168 + -15x + -15x2 = -168 + 168 + 15x + -15x + 15x2 + -15x2 Combine like terms: -168 + 168 = 0 168 + -15x + -15x2 = 0 + 15x + -15x + 15x2 + -15x2 168 + -15x + -15x2 = 15x + -15x + 15x2 + -15x2 Combine like terms: 15x + -15x = 0 168 + -15x + -15x2 = 0 + 15x2 + -15x2 168 + -15x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 168 + -15x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(56 + -5x + -5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(56 + -5x + -5x2)' equal to zero and attempt to solve: Simplifying 56 + -5x + -5x2 = 0 Solving 56 + -5x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -11.2 + x + x2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + x + 11.2 + x2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + x + x2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + x + x2 = 0 + 11.2 x + x2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 x + x2 = 11.2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 11.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 11.2 + 0.25 Combine like terms: 11.2 + 0.25 = 11.45 1.25 + x2 = 11.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 11.45 Calculate the square root of the right side: 3.383784863 Break this problem into two subproblems by setting (x + 0.5) equal to 3.383784863 and -3.383784863.Subproblem 1
x + 0.5 = 3.383784863 Simplifying x + 0.5 = 3.383784863 Reorder the terms: 0.5 + x = 3.383784863 Solving 0.5 + x = 3.383784863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.383784863 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.383784863 + -0.5 x = 3.383784863 + -0.5 Combine like terms: 3.383784863 + -0.5 = 2.883784863 x = 2.883784863 Simplifying x = 2.883784863Subproblem 2
x + 0.5 = -3.383784863 Simplifying x + 0.5 = -3.383784863 Reorder the terms: 0.5 + x = -3.383784863 Solving 0.5 + x = -3.383784863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.383784863 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.383784863 + -0.5 x = -3.383784863 + -0.5 Combine like terms: -3.383784863 + -0.5 = -3.883784863 x = -3.883784863 Simplifying x = -3.883784863Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.883784863, -3.883784863}Solution
x = {2.883784863, -3.883784863}
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