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Simplifying 4x2 + 56x + -285 = 0 Reorder the terms: -285 + 56x + 4x2 = 0 Solving -285 + 56x + 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'. -71.25 + 14x + x2 = 0 Move the constant term to the right: Add '71.25' to each side of the equation. -71.25 + 14x + 71.25 + x2 = 0 + 71.25 Reorder the terms: -71.25 + 71.25 + 14x + x2 = 0 + 71.25 Combine like terms: -71.25 + 71.25 = 0.00 0.00 + 14x + x2 = 0 + 71.25 14x + x2 = 0 + 71.25 Combine like terms: 0 + 71.25 = 71.25 14x + x2 = 71.25 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 71.25 + 49 Reorder the terms: 49 + 14x + x2 = 71.25 + 49 Combine like terms: 71.25 + 49 = 120.25 49 + 14x + x2 = 120.25 Factor a perfect square on the left side: (x + 7)(x + 7) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + 7) equal to 10.9658561 and -10.9658561.Subproblem 1
x + 7 = 10.9658561 Simplifying x + 7 = 10.9658561 Reorder the terms: 7 + x = 10.9658561 Solving 7 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 10.9658561 + -7 Combine like terms: 7 + -7 = 0 0 + x = 10.9658561 + -7 x = 10.9658561 + -7 Combine like terms: 10.9658561 + -7 = 3.9658561 x = 3.9658561 Simplifying x = 3.9658561Subproblem 2
x + 7 = -10.9658561 Simplifying x + 7 = -10.9658561 Reorder the terms: 7 + x = -10.9658561 Solving 7 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -10.9658561 + -7 Combine like terms: 7 + -7 = 0 0 + x = -10.9658561 + -7 x = -10.9658561 + -7 Combine like terms: -10.9658561 + -7 = -17.9658561 x = -17.9658561 Simplifying x = -17.9658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9658561, -17.9658561}
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