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Simplifying 13x2 + 12x = 15 Reorder the terms: 12x + 13x2 = 15 Solving 12x + 13x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 12x + 13x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 12x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -1.153846154 + 0.9230769231x + x2 = 0 Move the constant term to the right: Add '1.153846154' to each side of the equation. -1.153846154 + 0.9230769231x + 1.153846154 + x2 = 0 + 1.153846154 Reorder the terms: -1.153846154 + 1.153846154 + 0.9230769231x + x2 = 0 + 1.153846154 Combine like terms: -1.153846154 + 1.153846154 = 0.000000000 0.000000000 + 0.9230769231x + x2 = 0 + 1.153846154 0.9230769231x + x2 = 0 + 1.153846154 Combine like terms: 0 + 1.153846154 = 1.153846154 0.9230769231x + x2 = 1.153846154 The x term is 0.9230769231x. Take half its coefficient (0.4615384616). Square it (0.2130177515) and add it to both sides. Add '0.2130177515' to each side of the equation. 0.9230769231x + 0.2130177515 + x2 = 1.153846154 + 0.2130177515 Reorder the terms: 0.2130177515 + 0.9230769231x + x2 = 1.153846154 + 0.2130177515 Combine like terms: 1.153846154 + 0.2130177515 = 1.3668639055 0.2130177515 + 0.9230769231x + x2 = 1.3668639055 Factor a perfect square on the left side: (x + 0.4615384616)(x + 0.4615384616) = 1.3668639055 Calculate the square root of the right side: 1.16912955 Break this problem into two subproblems by setting (x + 0.4615384616) equal to 1.16912955 and -1.16912955.Subproblem 1
x + 0.4615384616 = 1.16912955 Simplifying x + 0.4615384616 = 1.16912955 Reorder the terms: 0.4615384616 + x = 1.16912955 Solving 0.4615384616 + x = 1.16912955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4615384616' to each side of the equation. 0.4615384616 + -0.4615384616 + x = 1.16912955 + -0.4615384616 Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000 0.0000000000 + x = 1.16912955 + -0.4615384616 x = 1.16912955 + -0.4615384616 Combine like terms: 1.16912955 + -0.4615384616 = 0.7075910884 x = 0.7075910884 Simplifying x = 0.7075910884Subproblem 2
x + 0.4615384616 = -1.16912955 Simplifying x + 0.4615384616 = -1.16912955 Reorder the terms: 0.4615384616 + x = -1.16912955 Solving 0.4615384616 + x = -1.16912955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4615384616' to each side of the equation. 0.4615384616 + -0.4615384616 + x = -1.16912955 + -0.4615384616 Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000 0.0000000000 + x = -1.16912955 + -0.4615384616 x = -1.16912955 + -0.4615384616 Combine like terms: -1.16912955 + -0.4615384616 = -1.6306680116 x = -1.6306680116 Simplifying x = -1.6306680116Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7075910884, -1.6306680116}
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