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Simplifying 2x2 + 28x + -147 = 0 Reorder the terms: -147 + 28x + 2x2 = 0 Solving -147 + 28x + 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'. -73.5 + 14x + x2 = 0 Move the constant term to the right: Add '73.5' to each side of the equation. -73.5 + 14x + 73.5 + x2 = 0 + 73.5 Reorder the terms: -73.5 + 73.5 + 14x + x2 = 0 + 73.5 Combine like terms: -73.5 + 73.5 = 0.0 0.0 + 14x + x2 = 0 + 73.5 14x + x2 = 0 + 73.5 Combine like terms: 0 + 73.5 = 73.5 14x + x2 = 73.5 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 = 73.5 + 49 Reorder the terms: 49 + 14x + x2 = 73.5 + 49 Combine like terms: 73.5 + 49 = 122.5 49 + 14x + x2 = 122.5 Factor a perfect square on the left side: (x + 7)(x + 7) = 122.5 Calculate the square root of the right side: 11.067971811 Break this problem into two subproblems by setting (x + 7) equal to 11.067971811 and -11.067971811.Subproblem 1
x + 7 = 11.067971811 Simplifying x + 7 = 11.067971811 Reorder the terms: 7 + x = 11.067971811 Solving 7 + x = 11.067971811 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 = 11.067971811 + -7 Combine like terms: 7 + -7 = 0 0 + x = 11.067971811 + -7 x = 11.067971811 + -7 Combine like terms: 11.067971811 + -7 = 4.067971811 x = 4.067971811 Simplifying x = 4.067971811Subproblem 2
x + 7 = -11.067971811 Simplifying x + 7 = -11.067971811 Reorder the terms: 7 + x = -11.067971811 Solving 7 + x = -11.067971811 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 = -11.067971811 + -7 Combine like terms: 7 + -7 = 0 0 + x = -11.067971811 + -7 x = -11.067971811 + -7 Combine like terms: -11.067971811 + -7 = -18.067971811 x = -18.067971811 Simplifying x = -18.067971811Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.067971811, -18.067971811}
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