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Simplifying 7x2 + 20x + 14 = 0 Reorder the terms: 14 + 20x + 7x2 = 0 Solving 14 + 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'. 2 + 2.857142857x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 2.857142857x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 2.857142857x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 2.857142857x + x2 = 0 + -2 2.857142857x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 2.857142857x + x2 = -2 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 = -2 + 2.040816328 Reorder the terms: 2.040816328 + 2.857142857x + x2 = -2 + 2.040816328 Combine like terms: -2 + 2.040816328 = 0.040816328 2.040816328 + 2.857142857x + x2 = 0.040816328 Factor a perfect square on the left side: (x + 1.428571429)(x + 1.428571429) = 0.040816328 Calculate the square root of the right side: 0.202030513 Break this problem into two subproblems by setting (x + 1.428571429) equal to 0.202030513 and -0.202030513.Subproblem 1
x + 1.428571429 = 0.202030513 Simplifying x + 1.428571429 = 0.202030513 Reorder the terms: 1.428571429 + x = 0.202030513 Solving 1.428571429 + x = 0.202030513 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 = 0.202030513 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = 0.202030513 + -1.428571429 x = 0.202030513 + -1.428571429 Combine like terms: 0.202030513 + -1.428571429 = -1.226540916 x = -1.226540916 Simplifying x = -1.226540916Subproblem 2
x + 1.428571429 = -0.202030513 Simplifying x + 1.428571429 = -0.202030513 Reorder the terms: 1.428571429 + x = -0.202030513 Solving 1.428571429 + x = -0.202030513 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 = -0.202030513 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = -0.202030513 + -1.428571429 x = -0.202030513 + -1.428571429 Combine like terms: -0.202030513 + -1.428571429 = -1.630601942 x = -1.630601942 Simplifying x = -1.630601942Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.226540916, -1.630601942}
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