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Simplifying 5x2 + 2x = 195 Reorder the terms: 2x + 5x2 = 195 Solving 2x + 5x2 = 195 Solving for variable 'x'. Reorder the terms: -195 + 2x + 5x2 = 195 + -195 Combine like terms: 195 + -195 = 0 -195 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -39 + 0.4x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + 0.4x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 0.4x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 0.4x + x2 = 0 + 39 0.4x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 0.4x + x2 = 39 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 = 39 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 39 + 0.04 Combine like terms: 39 + 0.04 = 39.04 0.04 + 0.4x + x2 = 39.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 39.04 Calculate the square root of the right side: 6.248199741 Break this problem into two subproblems by setting (x + 0.2) equal to 6.248199741 and -6.248199741.Subproblem 1
x + 0.2 = 6.248199741 Simplifying x + 0.2 = 6.248199741 Reorder the terms: 0.2 + x = 6.248199741 Solving 0.2 + x = 6.248199741 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 = 6.248199741 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 6.248199741 + -0.2 x = 6.248199741 + -0.2 Combine like terms: 6.248199741 + -0.2 = 6.048199741 x = 6.048199741 Simplifying x = 6.048199741Subproblem 2
x + 0.2 = -6.248199741 Simplifying x + 0.2 = -6.248199741 Reorder the terms: 0.2 + x = -6.248199741 Solving 0.2 + x = -6.248199741 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 = -6.248199741 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -6.248199741 + -0.2 x = -6.248199741 + -0.2 Combine like terms: -6.248199741 + -0.2 = -6.448199741 x = -6.448199741 Simplifying x = -6.448199741Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.048199741, -6.448199741}
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