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Simplifying 5x2 + 2x = 38 Reorder the terms: 2x + 5x2 = 38 Solving 2x + 5x2 = 38 Solving for variable 'x'. Reorder the terms: -38 + 2x + 5x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.6 + 0.4x + x2 = 0 Move the constant term to the right: Add '7.6' to each side of the equation. -7.6 + 0.4x + 7.6 + x2 = 0 + 7.6 Reorder the terms: -7.6 + 7.6 + 0.4x + x2 = 0 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + 0.4x + x2 = 0 + 7.6 0.4x + x2 = 0 + 7.6 Combine like terms: 0 + 7.6 = 7.6 0.4x + x2 = 7.6 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 = 7.6 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 7.6 + 0.04 Combine like terms: 7.6 + 0.04 = 7.64 0.04 + 0.4x + x2 = 7.64 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 7.64 Calculate the square root of the right side: 2.764054992 Break this problem into two subproblems by setting (x + 0.2) equal to 2.764054992 and -2.764054992.Subproblem 1
x + 0.2 = 2.764054992 Simplifying x + 0.2 = 2.764054992 Reorder the terms: 0.2 + x = 2.764054992 Solving 0.2 + x = 2.764054992 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 = 2.764054992 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 2.764054992 + -0.2 x = 2.764054992 + -0.2 Combine like terms: 2.764054992 + -0.2 = 2.564054992 x = 2.564054992 Simplifying x = 2.564054992Subproblem 2
x + 0.2 = -2.764054992 Simplifying x + 0.2 = -2.764054992 Reorder the terms: 0.2 + x = -2.764054992 Solving 0.2 + x = -2.764054992 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 = -2.764054992 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -2.764054992 + -0.2 x = -2.764054992 + -0.2 Combine like terms: -2.764054992 + -0.2 = -2.964054992 x = -2.964054992 Simplifying x = -2.964054992Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.564054992, -2.964054992}
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