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Simplifying 2x2 + 3x = 78 Reorder the terms: 3x + 2x2 = 78 Solving 3x + 2x2 = 78 Solving for variable 'x'. Reorder the terms: -78 + 3x + 2x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -78 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -39 + 1.5x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + 1.5x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 1.5x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 1.5x + x2 = 0 + 39 1.5x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 1.5x + x2 = 39 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 39 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 39 + 0.5625 Combine like terms: 39 + 0.5625 = 39.5625 0.5625 + 1.5x + x2 = 39.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 39.5625 Calculate the square root of the right side: 6.289872813 Break this problem into two subproblems by setting (x + 0.75) equal to 6.289872813 and -6.289872813.Subproblem 1
x + 0.75 = 6.289872813 Simplifying x + 0.75 = 6.289872813 Reorder the terms: 0.75 + x = 6.289872813 Solving 0.75 + x = 6.289872813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 6.289872813 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 6.289872813 + -0.75 x = 6.289872813 + -0.75 Combine like terms: 6.289872813 + -0.75 = 5.539872813 x = 5.539872813 Simplifying x = 5.539872813Subproblem 2
x + 0.75 = -6.289872813 Simplifying x + 0.75 = -6.289872813 Reorder the terms: 0.75 + x = -6.289872813 Solving 0.75 + x = -6.289872813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -6.289872813 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -6.289872813 + -0.75 x = -6.289872813 + -0.75 Combine like terms: -6.289872813 + -0.75 = -7.039872813 x = -7.039872813 Simplifying x = -7.039872813Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.539872813, -7.039872813}
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