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Simplifying 13x2 + 8x + -243 = 0 Reorder the terms: -243 + 8x + 13x2 = 0 Solving -243 + 8x + 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'. -18.69230769 + 0.6153846154x + x2 = 0 Move the constant term to the right: Add '18.69230769' to each side of the equation. -18.69230769 + 0.6153846154x + 18.69230769 + x2 = 0 + 18.69230769 Reorder the terms: -18.69230769 + 18.69230769 + 0.6153846154x + x2 = 0 + 18.69230769 Combine like terms: -18.69230769 + 18.69230769 = 0.00000000 0.00000000 + 0.6153846154x + x2 = 0 + 18.69230769 0.6153846154x + x2 = 0 + 18.69230769 Combine like terms: 0 + 18.69230769 = 18.69230769 0.6153846154x + x2 = 18.69230769 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 = 18.69230769 + 0.09467455622 Reorder the terms: 0.09467455622 + 0.6153846154x + x2 = 18.69230769 + 0.09467455622 Combine like terms: 18.69230769 + 0.09467455622 = 18.78698224622 0.09467455622 + 0.6153846154x + x2 = 18.78698224622 Factor a perfect square on the left side: (x + 0.3076923077)(x + 0.3076923077) = 18.78698224622 Calculate the square root of the right side: 4.334395257 Break this problem into two subproblems by setting (x + 0.3076923077) equal to 4.334395257 and -4.334395257.Subproblem 1
x + 0.3076923077 = 4.334395257 Simplifying x + 0.3076923077 = 4.334395257 Reorder the terms: 0.3076923077 + x = 4.334395257 Solving 0.3076923077 + x = 4.334395257 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 = 4.334395257 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = 4.334395257 + -0.3076923077 x = 4.334395257 + -0.3076923077 Combine like terms: 4.334395257 + -0.3076923077 = 4.0267029493 x = 4.0267029493 Simplifying x = 4.0267029493Subproblem 2
x + 0.3076923077 = -4.334395257 Simplifying x + 0.3076923077 = -4.334395257 Reorder the terms: 0.3076923077 + x = -4.334395257 Solving 0.3076923077 + x = -4.334395257 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 = -4.334395257 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = -4.334395257 + -0.3076923077 x = -4.334395257 + -0.3076923077 Combine like terms: -4.334395257 + -0.3076923077 = -4.6420875647 x = -4.6420875647 Simplifying x = -4.6420875647Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.0267029493, -4.6420875647}
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