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Simplifying 2x2 + 3x + -28 = 0 Reorder the terms: -28 + 3x + 2x2 = 0 Solving -28 + 3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14 + 1.5x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 1.5x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 1.5x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 1.5x + x2 = 0 + 14 1.5x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 1.5x + x2 = 14 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 = 14 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 14 + 0.5625 Combine like terms: 14 + 0.5625 = 14.5625 0.5625 + 1.5x + x2 = 14.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (x + 0.75) equal to 3.816084381 and -3.816084381.Subproblem 1
x + 0.75 = 3.816084381 Simplifying x + 0.75 = 3.816084381 Reorder the terms: 0.75 + x = 3.816084381 Solving 0.75 + x = 3.816084381 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 = 3.816084381 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 3.816084381 + -0.75 x = 3.816084381 + -0.75 Combine like terms: 3.816084381 + -0.75 = 3.066084381 x = 3.066084381 Simplifying x = 3.066084381Subproblem 2
x + 0.75 = -3.816084381 Simplifying x + 0.75 = -3.816084381 Reorder the terms: 0.75 + x = -3.816084381 Solving 0.75 + x = -3.816084381 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 = -3.816084381 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -3.816084381 + -0.75 x = -3.816084381 + -0.75 Combine like terms: -3.816084381 + -0.75 = -4.566084381 x = -4.566084381 Simplifying x = -4.566084381Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.066084381, -4.566084381}
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