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Simplifying 13x2 + 8x = 75 Reorder the terms: 8x + 13x2 = 75 Solving 8x + 13x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + 8x + 13x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 8x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -5.769230769 + 0.6153846154x + x2 = 0 Move the constant term to the right: Add '5.769230769' to each side of the equation. -5.769230769 + 0.6153846154x + 5.769230769 + x2 = 0 + 5.769230769 Reorder the terms: -5.769230769 + 5.769230769 + 0.6153846154x + x2 = 0 + 5.769230769 Combine like terms: -5.769230769 + 5.769230769 = 0.000000000 0.000000000 + 0.6153846154x + x2 = 0 + 5.769230769 0.6153846154x + x2 = 0 + 5.769230769 Combine like terms: 0 + 5.769230769 = 5.769230769 0.6153846154x + x2 = 5.769230769 The x term is 0.6153846154x. Take half its coefficient (0.3076923077). Square it (0.09467455622) and add it to both sides. Add '0.09467455622' to each side of the equation. 0.6153846154x + 0.09467455622 + x2 = 5.769230769 + 0.09467455622 Reorder the terms: 0.09467455622 + 0.6153846154x + x2 = 5.769230769 + 0.09467455622 Combine like terms: 5.769230769 + 0.09467455622 = 5.86390532522 0.09467455622 + 0.6153846154x + x2 = 5.86390532522 Factor a perfect square on the left side: (x + 0.3076923077)(x + 0.3076923077) = 5.86390532522 Calculate the square root of the right side: 2.421550191 Break this problem into two subproblems by setting (x + 0.3076923077) equal to 2.421550191 and -2.421550191.Subproblem 1
x + 0.3076923077 = 2.421550191 Simplifying x + 0.3076923077 = 2.421550191 Reorder the terms: 0.3076923077 + x = 2.421550191 Solving 0.3076923077 + x = 2.421550191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3076923077' to each side of the equation. 0.3076923077 + -0.3076923077 + x = 2.421550191 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = 2.421550191 + -0.3076923077 x = 2.421550191 + -0.3076923077 Combine like terms: 2.421550191 + -0.3076923077 = 2.1138578833 x = 2.1138578833 Simplifying x = 2.1138578833Subproblem 2
x + 0.3076923077 = -2.421550191 Simplifying x + 0.3076923077 = -2.421550191 Reorder the terms: 0.3076923077 + x = -2.421550191 Solving 0.3076923077 + x = -2.421550191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3076923077' to each side of the equation. 0.3076923077 + -0.3076923077 + x = -2.421550191 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = -2.421550191 + -0.3076923077 x = -2.421550191 + -0.3076923077 Combine like terms: -2.421550191 + -0.3076923077 = -2.7292424987 x = -2.7292424987 Simplifying x = -2.7292424987Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1138578833, -2.7292424987}
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