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Simplifying 5x2 + 5x = 234 Reorder the terms: 5x + 5x2 = 234 Solving 5x + 5x2 = 234 Solving for variable 'x'. Reorder the terms: -234 + 5x + 5x2 = 234 + -234 Combine like terms: 234 + -234 = 0 -234 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -46.8 + x + x2 = 0 Move the constant term to the right: Add '46.8' to each side of the equation. -46.8 + x + 46.8 + x2 = 0 + 46.8 Reorder the terms: -46.8 + 46.8 + x + x2 = 0 + 46.8 Combine like terms: -46.8 + 46.8 = 0.0 0.0 + x + x2 = 0 + 46.8 x + x2 = 0 + 46.8 Combine like terms: 0 + 46.8 = 46.8 x + x2 = 46.8 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 46.8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 46.8 + 0.25 Combine like terms: 46.8 + 0.25 = 47.05 1.25 + x2 = 47.05 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 47.05 Calculate the square root of the right side: 6.859300256 Break this problem into two subproblems by setting (x + 0.5) equal to 6.859300256 and -6.859300256.Subproblem 1
x + 0.5 = 6.859300256 Simplifying x + 0.5 = 6.859300256 Reorder the terms: 0.5 + x = 6.859300256 Solving 0.5 + x = 6.859300256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.859300256 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.859300256 + -0.5 x = 6.859300256 + -0.5 Combine like terms: 6.859300256 + -0.5 = 6.359300256 x = 6.359300256 Simplifying x = 6.359300256Subproblem 2
x + 0.5 = -6.859300256 Simplifying x + 0.5 = -6.859300256 Reorder the terms: 0.5 + x = -6.859300256 Solving 0.5 + x = -6.859300256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.859300256 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.859300256 + -0.5 x = -6.859300256 + -0.5 Combine like terms: -6.859300256 + -0.5 = -7.359300256 x = -7.359300256 Simplifying x = -7.359300256Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.359300256, -7.359300256}
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