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Simplifying 5x2 + 2x = 56 Reorder the terms: 2x + 5x2 = 56 Solving 2x + 5x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + 2x + 5x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -11.2 + 0.4x + x2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + 0.4x + 11.2 + x2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + 0.4x + x2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + 0.4x + x2 = 0 + 11.2 0.4x + x2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 0.4x + x2 = 11.2 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 = 11.2 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 11.2 + 0.04 Combine like terms: 11.2 + 0.04 = 11.24 0.04 + 0.4x + x2 = 11.24 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 11.24 Calculate the square root of the right side: 3.352610923 Break this problem into two subproblems by setting (x + 0.2) equal to 3.352610923 and -3.352610923.Subproblem 1
x + 0.2 = 3.352610923 Simplifying x + 0.2 = 3.352610923 Reorder the terms: 0.2 + x = 3.352610923 Solving 0.2 + x = 3.352610923 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 = 3.352610923 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 3.352610923 + -0.2 x = 3.352610923 + -0.2 Combine like terms: 3.352610923 + -0.2 = 3.152610923 x = 3.152610923 Simplifying x = 3.152610923Subproblem 2
x + 0.2 = -3.352610923 Simplifying x + 0.2 = -3.352610923 Reorder the terms: 0.2 + x = -3.352610923 Solving 0.2 + x = -3.352610923 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 = -3.352610923 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -3.352610923 + -0.2 x = -3.352610923 + -0.2 Combine like terms: -3.352610923 + -0.2 = -3.552610923 x = -3.552610923 Simplifying x = -3.552610923Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.152610923, -3.552610923}
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