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Simplifying 7x2 + 20x + -8 = 0 Reorder the terms: -8 + 20x + 7x2 = 0 Solving -8 + 20x + 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 + 2.857142857x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 2.857142857x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 2.857142857x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 2.857142857x + x2 = 0 + 1.142857143 2.857142857x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 2.857142857x + x2 = 1.142857143 The x term is 2.857142857x. Take half its coefficient (1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. 2.857142857x + 2.040816328 + x2 = 1.142857143 + 2.040816328 Reorder the terms: 2.040816328 + 2.857142857x + x2 = 1.142857143 + 2.040816328 Combine like terms: 1.142857143 + 2.040816328 = 3.183673471 2.040816328 + 2.857142857x + x2 = 3.183673471 Factor a perfect square on the left side: (x + 1.428571429)(x + 1.428571429) = 3.183673471 Calculate the square root of the right side: 1.784285143 Break this problem into two subproblems by setting (x + 1.428571429) equal to 1.784285143 and -1.784285143.Subproblem 1
x + 1.428571429 = 1.784285143 Simplifying x + 1.428571429 = 1.784285143 Reorder the terms: 1.428571429 + x = 1.784285143 Solving 1.428571429 + x = 1.784285143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = 1.784285143 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = 1.784285143 + -1.428571429 x = 1.784285143 + -1.428571429 Combine like terms: 1.784285143 + -1.428571429 = 0.355713714 x = 0.355713714 Simplifying x = 0.355713714Subproblem 2
x + 1.428571429 = -1.784285143 Simplifying x + 1.428571429 = -1.784285143 Reorder the terms: 1.428571429 + x = -1.784285143 Solving 1.428571429 + x = -1.784285143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = -1.784285143 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = -1.784285143 + -1.428571429 x = -1.784285143 + -1.428571429 Combine like terms: -1.784285143 + -1.428571429 = -3.212856572 x = -3.212856572 Simplifying x = -3.212856572Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.355713714, -3.212856572}
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