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Simplifying 5x2 + 2x = 80 Reorder the terms: 2x + 5x2 = 80 Solving 2x + 5x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + 2x + 5x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -16 + 0.4x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 0.4x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 0.4x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 0.4x + x2 = 0 + 16 0.4x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 0.4x + x2 = 16 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 = 16 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 16 + 0.04 Combine like terms: 16 + 0.04 = 16.04 0.04 + 0.4x + x2 = 16.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 16.04 Calculate the square root of the right side: 4.004996879 Break this problem into two subproblems by setting (x + 0.2) equal to 4.004996879 and -4.004996879.Subproblem 1
x + 0.2 = 4.004996879 Simplifying x + 0.2 = 4.004996879 Reorder the terms: 0.2 + x = 4.004996879 Solving 0.2 + x = 4.004996879 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 = 4.004996879 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 4.004996879 + -0.2 x = 4.004996879 + -0.2 Combine like terms: 4.004996879 + -0.2 = 3.804996879 x = 3.804996879 Simplifying x = 3.804996879Subproblem 2
x + 0.2 = -4.004996879 Simplifying x + 0.2 = -4.004996879 Reorder the terms: 0.2 + x = -4.004996879 Solving 0.2 + x = -4.004996879 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 = -4.004996879 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -4.004996879 + -0.2 x = -4.004996879 + -0.2 Combine like terms: -4.004996879 + -0.2 = -4.204996879 x = -4.204996879 Simplifying x = -4.204996879Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.804996879, -4.204996879}
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