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Simplifying 7x2 + 27x + -8 = 0 Reorder the terms: -8 + 27x + 7x2 = 0 Solving -8 + 27x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 3.857142857x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 3.857142857x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 3.857142857x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 3.857142857x + x2 = 0 + 1.142857143 3.857142857x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 3.857142857x + x2 = 1.142857143 The x term is 3.857142857x. Take half its coefficient (1.928571429). Square it (3.719387757) and add it to both sides. Add '3.719387757' to each side of the equation. 3.857142857x + 3.719387757 + x2 = 1.142857143 + 3.719387757 Reorder the terms: 3.719387757 + 3.857142857x + x2 = 1.142857143 + 3.719387757 Combine like terms: 1.142857143 + 3.719387757 = 4.8622449 3.719387757 + 3.857142857x + x2 = 4.8622449 Factor a perfect square on the left side: (x + 1.928571429)(x + 1.928571429) = 4.8622449 Calculate the square root of the right side: 2.205049863 Break this problem into two subproblems by setting (x + 1.928571429) equal to 2.205049863 and -2.205049863.Subproblem 1
x + 1.928571429 = 2.205049863 Simplifying x + 1.928571429 = 2.205049863 Reorder the terms: 1.928571429 + x = 2.205049863 Solving 1.928571429 + x = 2.205049863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.928571429' to each side of the equation. 1.928571429 + -1.928571429 + x = 2.205049863 + -1.928571429 Combine like terms: 1.928571429 + -1.928571429 = 0.000000000 0.000000000 + x = 2.205049863 + -1.928571429 x = 2.205049863 + -1.928571429 Combine like terms: 2.205049863 + -1.928571429 = 0.276478434 x = 0.276478434 Simplifying x = 0.276478434Subproblem 2
x + 1.928571429 = -2.205049863 Simplifying x + 1.928571429 = -2.205049863 Reorder the terms: 1.928571429 + x = -2.205049863 Solving 1.928571429 + x = -2.205049863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.928571429' to each side of the equation. 1.928571429 + -1.928571429 + x = -2.205049863 + -1.928571429 Combine like terms: 1.928571429 + -1.928571429 = 0.000000000 0.000000000 + x = -2.205049863 + -1.928571429 x = -2.205049863 + -1.928571429 Combine like terms: -2.205049863 + -1.928571429 = -4.133621292 x = -4.133621292 Simplifying x = -4.133621292Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.276478434, -4.133621292}
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