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Simplifying 14x2 + -8x + -9 = 0 Reorder the terms: -9 + -8x + 14x2 = 0 Solving -9 + -8x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.6428571429 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.6428571429' to each side of the equation. -0.6428571429 + -0.5714285714x + 0.6428571429 + x2 = 0 + 0.6428571429 Reorder the terms: -0.6428571429 + 0.6428571429 + -0.5714285714x + x2 = 0 + 0.6428571429 Combine like terms: -0.6428571429 + 0.6428571429 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + 0.6428571429 -0.5714285714x + x2 = 0 + 0.6428571429 Combine like terms: 0 + 0.6428571429 = 0.6428571429 -0.5714285714x + x2 = 0.6428571429 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 0.6428571429 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 0.6428571429 + 0.08163265305 Combine like terms: 0.6428571429 + 0.08163265305 = 0.72448979595 0.08163265305 + -0.5714285714x + x2 = 0.72448979595 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 0.72448979595 Calculate the square root of the right side: 0.851169663 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 0.851169663 and -0.851169663.Subproblem 1
x + -0.2857142857 = 0.851169663 Simplifying x + -0.2857142857 = 0.851169663 Reorder the terms: -0.2857142857 + x = 0.851169663 Solving -0.2857142857 + x = 0.851169663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 0.851169663 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.851169663 + 0.2857142857 x = 0.851169663 + 0.2857142857 Combine like terms: 0.851169663 + 0.2857142857 = 1.1368839487 x = 1.1368839487 Simplifying x = 1.1368839487Subproblem 2
x + -0.2857142857 = -0.851169663 Simplifying x + -0.2857142857 = -0.851169663 Reorder the terms: -0.2857142857 + x = -0.851169663 Solving -0.2857142857 + x = -0.851169663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -0.851169663 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.851169663 + 0.2857142857 x = -0.851169663 + 0.2857142857 Combine like terms: -0.851169663 + 0.2857142857 = -0.5654553773 x = -0.5654553773 Simplifying x = -0.5654553773Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1368839487, -0.5654553773}
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