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Simplifying 15x2 + 69x + 12 = 0 Reorder the terms: 12 + 69x + 15x2 = 0 Solving 12 + 69x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 23x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 23x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + 23x + 5x2 = 0 Solving 4 + 23x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 4.6x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 4.6x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 4.6x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 4.6x + x2 = 0 + -0.8 4.6x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 4.6x + x2 = -0.8 The x term is 4.6x. Take half its coefficient (2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. 4.6x + 5.29 + x2 = -0.8 + 5.29 Reorder the terms: 5.29 + 4.6x + x2 = -0.8 + 5.29 Combine like terms: -0.8 + 5.29 = 4.49 5.29 + 4.6x + x2 = 4.49 Factor a perfect square on the left side: (x + 2.3)(x + 2.3) = 4.49 Calculate the square root of the right side: 2.11896201 Break this problem into two subproblems by setting (x + 2.3) equal to 2.11896201 and -2.11896201.Subproblem 1
x + 2.3 = 2.11896201 Simplifying x + 2.3 = 2.11896201 Reorder the terms: 2.3 + x = 2.11896201 Solving 2.3 + x = 2.11896201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = 2.11896201 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = 2.11896201 + -2.3 x = 2.11896201 + -2.3 Combine like terms: 2.11896201 + -2.3 = -0.18103799 x = -0.18103799 Simplifying x = -0.18103799Subproblem 2
x + 2.3 = -2.11896201 Simplifying x + 2.3 = -2.11896201 Reorder the terms: 2.3 + x = -2.11896201 Solving 2.3 + x = -2.11896201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = -2.11896201 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = -2.11896201 + -2.3 x = -2.11896201 + -2.3 Combine like terms: -2.11896201 + -2.3 = -4.41896201 x = -4.41896201 Simplifying x = -4.41896201Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.18103799, -4.41896201}Solution
x = {-0.18103799, -4.41896201}
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