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Simplifying 13x2 + 28x + 12 = 0 Reorder the terms: 12 + 28x + 13x2 = 0 Solving 12 + 28x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.9230769231 + 2.153846154x + x2 = 0 Move the constant term to the right: Add '-0.9230769231' to each side of the equation. 0.9230769231 + 2.153846154x + -0.9230769231 + x2 = 0 + -0.9230769231 Reorder the terms: 0.9230769231 + -0.9230769231 + 2.153846154x + x2 = 0 + -0.9230769231 Combine like terms: 0.9230769231 + -0.9230769231 = 0.0000000000 0.0000000000 + 2.153846154x + x2 = 0 + -0.9230769231 2.153846154x + x2 = 0 + -0.9230769231 Combine like terms: 0 + -0.9230769231 = -0.9230769231 2.153846154x + x2 = -0.9230769231 The x term is 2.153846154x. Take half its coefficient (1.076923077). Square it (1.159763314) and add it to both sides. Add '1.159763314' to each side of the equation. 2.153846154x + 1.159763314 + x2 = -0.9230769231 + 1.159763314 Reorder the terms: 1.159763314 + 2.153846154x + x2 = -0.9230769231 + 1.159763314 Combine like terms: -0.9230769231 + 1.159763314 = 0.2366863909 1.159763314 + 2.153846154x + x2 = 0.2366863909 Factor a perfect square on the left side: (x + 1.076923077)(x + 1.076923077) = 0.2366863909 Calculate the square root of the right side: 0.486504256 Break this problem into two subproblems by setting (x + 1.076923077) equal to 0.486504256 and -0.486504256.Subproblem 1
x + 1.076923077 = 0.486504256 Simplifying x + 1.076923077 = 0.486504256 Reorder the terms: 1.076923077 + x = 0.486504256 Solving 1.076923077 + x = 0.486504256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.076923077' to each side of the equation. 1.076923077 + -1.076923077 + x = 0.486504256 + -1.076923077 Combine like terms: 1.076923077 + -1.076923077 = 0.000000000 0.000000000 + x = 0.486504256 + -1.076923077 x = 0.486504256 + -1.076923077 Combine like terms: 0.486504256 + -1.076923077 = -0.590418821 x = -0.590418821 Simplifying x = -0.590418821Subproblem 2
x + 1.076923077 = -0.486504256 Simplifying x + 1.076923077 = -0.486504256 Reorder the terms: 1.076923077 + x = -0.486504256 Solving 1.076923077 + x = -0.486504256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.076923077' to each side of the equation. 1.076923077 + -1.076923077 + x = -0.486504256 + -1.076923077 Combine like terms: 1.076923077 + -1.076923077 = 0.000000000 0.000000000 + x = -0.486504256 + -1.076923077 x = -0.486504256 + -1.076923077 Combine like terms: -0.486504256 + -1.076923077 = -1.563427333 x = -1.563427333 Simplifying x = -1.563427333Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.590418821, -1.563427333}
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