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Simplifying 5x2 + -2x + -22 = 0 Reorder the terms: -22 + -2x + 5x2 = 0 Solving -22 + -2x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.4 + -0.4x + x2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + -0.4x + 4.4 + x2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + -0.4x + x2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + -0.4x + x2 = 0 + 4.4 -0.4x + x2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 -0.4x + x2 = 4.4 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 4.4 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 4.4 + 0.04 Combine like terms: 4.4 + 0.04 = 4.44 0.04 + -0.4x + x2 = 4.44 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 4.44 Calculate the square root of the right side: 2.107130751 Break this problem into two subproblems by setting (x + -0.2) equal to 2.107130751 and -2.107130751.Subproblem 1
x + -0.2 = 2.107130751 Simplifying x + -0.2 = 2.107130751 Reorder the terms: -0.2 + x = 2.107130751 Solving -0.2 + x = 2.107130751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 2.107130751 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 2.107130751 + 0.2 x = 2.107130751 + 0.2 Combine like terms: 2.107130751 + 0.2 = 2.307130751 x = 2.307130751 Simplifying x = 2.307130751Subproblem 2
x + -0.2 = -2.107130751 Simplifying x + -0.2 = -2.107130751 Reorder the terms: -0.2 + x = -2.107130751 Solving -0.2 + x = -2.107130751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -2.107130751 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -2.107130751 + 0.2 x = -2.107130751 + 0.2 Combine like terms: -2.107130751 + 0.2 = -1.907130751 x = -1.907130751 Simplifying x = -1.907130751Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.307130751, -1.907130751}
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