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Simplifying 28 + -7x2 + 2x = 0 Reorder the terms: 28 + 2x + -7x2 = 0 Solving 28 + 2x + -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'. -4 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.2857142857x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -0.2857142857x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.2857142857x + x2 = 0 + 4 -0.2857142857x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.2857142857x + x2 = 4 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 4 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 4 + 0.02040816328 Combine like terms: 4 + 0.02040816328 = 4.02040816328 0.02040816328 + -0.2857142857x + x2 = 4.02040816328 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 4.02040816328 Calculate the square root of the right side: 2.00509555 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 2.00509555 and -2.00509555.Subproblem 1
x + -0.1428571429 = 2.00509555 Simplifying x + -0.1428571429 = 2.00509555 Reorder the terms: -0.1428571429 + x = 2.00509555 Solving -0.1428571429 + x = 2.00509555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 2.00509555 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 2.00509555 + 0.1428571429 x = 2.00509555 + 0.1428571429 Combine like terms: 2.00509555 + 0.1428571429 = 2.1479526929 x = 2.1479526929 Simplifying x = 2.1479526929Subproblem 2
x + -0.1428571429 = -2.00509555 Simplifying x + -0.1428571429 = -2.00509555 Reorder the terms: -0.1428571429 + x = -2.00509555 Solving -0.1428571429 + x = -2.00509555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -2.00509555 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -2.00509555 + 0.1428571429 x = -2.00509555 + 0.1428571429 Combine like terms: -2.00509555 + 0.1428571429 = -1.8622384071 x = -1.8622384071 Simplifying x = -1.8622384071Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1479526929, -1.8622384071}
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