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Simplifying 0 = x2 + 28x + -1040 Reorder the terms: 0 = -1040 + 28x + x2 Solving 0 = -1040 + 28x + x2 Solving for variable 'x'. Combine like terms: 0 + 1040 = 1040 1040 + -28x + -1x2 = -1040 + 28x + x2 + 1040 + -28x + -1x2 Reorder the terms: 1040 + -28x + -1x2 = -1040 + 1040 + 28x + -28x + x2 + -1x2 Combine like terms: -1040 + 1040 = 0 1040 + -28x + -1x2 = 0 + 28x + -28x + x2 + -1x2 1040 + -28x + -1x2 = 28x + -28x + x2 + -1x2 Combine like terms: 28x + -28x = 0 1040 + -28x + -1x2 = 0 + x2 + -1x2 1040 + -28x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1040 + -28x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1040 + 28x + x2 = 0 Move the constant term to the right: Add '1040' to each side of the equation. -1040 + 28x + 1040 + x2 = 0 + 1040 Reorder the terms: -1040 + 1040 + 28x + x2 = 0 + 1040 Combine like terms: -1040 + 1040 = 0 0 + 28x + x2 = 0 + 1040 28x + x2 = 0 + 1040 Combine like terms: 0 + 1040 = 1040 28x + x2 = 1040 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 1040 + 196 Reorder the terms: 196 + 28x + x2 = 1040 + 196 Combine like terms: 1040 + 196 = 1236 196 + 28x + x2 = 1236 Factor a perfect square on the left side: (x + 14)(x + 14) = 1236 Calculate the square root of the right side: 35.156791662 Break this problem into two subproblems by setting (x + 14) equal to 35.156791662 and -35.156791662.Subproblem 1
x + 14 = 35.156791662 Simplifying x + 14 = 35.156791662 Reorder the terms: 14 + x = 35.156791662 Solving 14 + x = 35.156791662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 35.156791662 + -14 Combine like terms: 14 + -14 = 0 0 + x = 35.156791662 + -14 x = 35.156791662 + -14 Combine like terms: 35.156791662 + -14 = 21.156791662 x = 21.156791662 Simplifying x = 21.156791662Subproblem 2
x + 14 = -35.156791662 Simplifying x + 14 = -35.156791662 Reorder the terms: 14 + x = -35.156791662 Solving 14 + x = -35.156791662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -35.156791662 + -14 Combine like terms: 14 + -14 = 0 0 + x = -35.156791662 + -14 x = -35.156791662 + -14 Combine like terms: -35.156791662 + -14 = -49.156791662 x = -49.156791662 Simplifying x = -49.156791662Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.156791662, -49.156791662}
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