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Simplifying 4x2 + 39x + -42 = 0 Reorder the terms: -42 + 39x + 4x2 = 0 Solving -42 + 39x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.5 + 9.75x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 9.75x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 9.75x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 9.75x + x2 = 0 + 10.5 9.75x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 9.75x + x2 = 10.5 The x term is 9.75x. Take half its coefficient (4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. 9.75x + 23.765625 + x2 = 10.5 + 23.765625 Reorder the terms: 23.765625 + 9.75x + x2 = 10.5 + 23.765625 Combine like terms: 10.5 + 23.765625 = 34.265625 23.765625 + 9.75x + x2 = 34.265625 Factor a perfect square on the left side: (x + 4.875)(x + 4.875) = 34.265625 Calculate the square root of the right side: 5.853684737 Break this problem into two subproblems by setting (x + 4.875) equal to 5.853684737 and -5.853684737.Subproblem 1
x + 4.875 = 5.853684737 Simplifying x + 4.875 = 5.853684737 Reorder the terms: 4.875 + x = 5.853684737 Solving 4.875 + x = 5.853684737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.875' to each side of the equation. 4.875 + -4.875 + x = 5.853684737 + -4.875 Combine like terms: 4.875 + -4.875 = 0.000 0.000 + x = 5.853684737 + -4.875 x = 5.853684737 + -4.875 Combine like terms: 5.853684737 + -4.875 = 0.978684737 x = 0.978684737 Simplifying x = 0.978684737Subproblem 2
x + 4.875 = -5.853684737 Simplifying x + 4.875 = -5.853684737 Reorder the terms: 4.875 + x = -5.853684737 Solving 4.875 + x = -5.853684737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.875' to each side of the equation. 4.875 + -4.875 + x = -5.853684737 + -4.875 Combine like terms: 4.875 + -4.875 = 0.000 0.000 + x = -5.853684737 + -4.875 x = -5.853684737 + -4.875 Combine like terms: -5.853684737 + -4.875 = -10.728684737 x = -10.728684737 Simplifying x = -10.728684737Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.978684737, -10.728684737}
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