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Simplifying 2.1 + 5.2x + -1(2.1x2) = 0 Remove parenthesis around (2.1x2) 2.1 + 5.2x + -1 * 2.1x2 = 0 Multiply -1 * 2.1 2.1 + 5.2x + -2.1x2 = 0 Solving 2.1 + 5.2x + -2.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.1 the coefficient of the squared term: Divide each side by '-2.1'. -1 + -2.476190476x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.476190476x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.476190476x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.476190476x + x2 = 0 + 1 -2.476190476x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.476190476x + x2 = 1 The x term is -2.476190476x. Take half its coefficient (-1.238095238). Square it (1.532879818) and add it to both sides. Add '1.532879818' to each side of the equation. -2.476190476x + 1.532879818 + x2 = 1 + 1.532879818 Reorder the terms: 1.532879818 + -2.476190476x + x2 = 1 + 1.532879818 Combine like terms: 1 + 1.532879818 = 2.532879818 1.532879818 + -2.476190476x + x2 = 2.532879818 Factor a perfect square on the left side: (x + -1.238095238)(x + -1.238095238) = 2.532879818 Calculate the square root of the right side: 1.591502378 Break this problem into two subproblems by setting (x + -1.238095238) equal to 1.591502378 and -1.591502378.Subproblem 1
x + -1.238095238 = 1.591502378 Simplifying x + -1.238095238 = 1.591502378 Reorder the terms: -1.238095238 + x = 1.591502378 Solving -1.238095238 + x = 1.591502378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.238095238' to each side of the equation. -1.238095238 + 1.238095238 + x = 1.591502378 + 1.238095238 Combine like terms: -1.238095238 + 1.238095238 = 0.000000000 0.000000000 + x = 1.591502378 + 1.238095238 x = 1.591502378 + 1.238095238 Combine like terms: 1.591502378 + 1.238095238 = 2.829597616 x = 2.829597616 Simplifying x = 2.829597616Subproblem 2
x + -1.238095238 = -1.591502378 Simplifying x + -1.238095238 = -1.591502378 Reorder the terms: -1.238095238 + x = -1.591502378 Solving -1.238095238 + x = -1.591502378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.238095238' to each side of the equation. -1.238095238 + 1.238095238 + x = -1.591502378 + 1.238095238 Combine like terms: -1.238095238 + 1.238095238 = 0.000000000 0.000000000 + x = -1.591502378 + 1.238095238 x = -1.591502378 + 1.238095238 Combine like terms: -1.591502378 + 1.238095238 = -0.35340714 x = -0.35340714 Simplifying x = -0.35340714Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.829597616, -0.35340714}
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