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Simplifying 4x2 + 56x + 99 = 0 Reorder the terms: 99 + 56x + 4x2 = 0 Solving 99 + 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'. 24.75 + 14x + x2 = 0 Move the constant term to the right: Add '-24.75' to each side of the equation. 24.75 + 14x + -24.75 + x2 = 0 + -24.75 Reorder the terms: 24.75 + -24.75 + 14x + x2 = 0 + -24.75 Combine like terms: 24.75 + -24.75 = 0.00 0.00 + 14x + x2 = 0 + -24.75 14x + x2 = 0 + -24.75 Combine like terms: 0 + -24.75 = -24.75 14x + x2 = -24.75 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 = -24.75 + 49 Reorder the terms: 49 + 14x + x2 = -24.75 + 49 Combine like terms: -24.75 + 49 = 24.25 49 + 14x + x2 = 24.25 Factor a perfect square on the left side: (x + 7)(x + 7) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + 7) equal to 4.924428901 and -4.924428901.Subproblem 1
x + 7 = 4.924428901 Simplifying x + 7 = 4.924428901 Reorder the terms: 7 + x = 4.924428901 Solving 7 + x = 4.924428901 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 = 4.924428901 + -7 Combine like terms: 7 + -7 = 0 0 + x = 4.924428901 + -7 x = 4.924428901 + -7 Combine like terms: 4.924428901 + -7 = -2.075571099 x = -2.075571099 Simplifying x = -2.075571099Subproblem 2
x + 7 = -4.924428901 Simplifying x + 7 = -4.924428901 Reorder the terms: 7 + x = -4.924428901 Solving 7 + x = -4.924428901 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 = -4.924428901 + -7 Combine like terms: 7 + -7 = 0 0 + x = -4.924428901 + -7 x = -4.924428901 + -7 Combine like terms: -4.924428901 + -7 = -11.924428901 x = -11.924428901 Simplifying x = -11.924428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.075571099, -11.924428901}
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