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Simplifying 7x2 + 84x + -14400 = 0 Reorder the terms: -14400 + 84x + 7x2 = 0 Solving -14400 + 84x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2057.142857 + 12x + x2 = 0 Move the constant term to the right: Add '2057.142857' to each side of the equation. -2057.142857 + 12x + 2057.142857 + x2 = 0 + 2057.142857 Reorder the terms: -2057.142857 + 2057.142857 + 12x + x2 = 0 + 2057.142857 Combine like terms: -2057.142857 + 2057.142857 = 0.000000 0.000000 + 12x + x2 = 0 + 2057.142857 12x + x2 = 0 + 2057.142857 Combine like terms: 0 + 2057.142857 = 2057.142857 12x + x2 = 2057.142857 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 2057.142857 + 36 Reorder the terms: 36 + 12x + x2 = 2057.142857 + 36 Combine like terms: 2057.142857 + 36 = 2093.142857 36 + 12x + x2 = 2093.142857 Factor a perfect square on the left side: (x + 6)(x + 6) = 2093.142857 Calculate the square root of the right side: 45.75087821 Break this problem into two subproblems by setting (x + 6) equal to 45.75087821 and -45.75087821.Subproblem 1
x + 6 = 45.75087821 Simplifying x + 6 = 45.75087821 Reorder the terms: 6 + x = 45.75087821 Solving 6 + x = 45.75087821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 45.75087821 + -6 Combine like terms: 6 + -6 = 0 0 + x = 45.75087821 + -6 x = 45.75087821 + -6 Combine like terms: 45.75087821 + -6 = 39.75087821 x = 39.75087821 Simplifying x = 39.75087821Subproblem 2
x + 6 = -45.75087821 Simplifying x + 6 = -45.75087821 Reorder the terms: 6 + x = -45.75087821 Solving 6 + x = -45.75087821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -45.75087821 + -6 Combine like terms: 6 + -6 = 0 0 + x = -45.75087821 + -6 x = -45.75087821 + -6 Combine like terms: -45.75087821 + -6 = -51.75087821 x = -51.75087821 Simplifying x = -51.75087821Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.75087821, -51.75087821}
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