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Simplifying x2 + 28x + -40 = 0 Reorder the terms: -40 + 28x + x2 = 0 Solving -40 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 28x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 28x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 28x + x2 = 0 + 40 28x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 28x + x2 = 40 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 = 40 + 196 Reorder the terms: 196 + 28x + x2 = 40 + 196 Combine like terms: 40 + 196 = 236 196 + 28x + x2 = 236 Factor a perfect square on the left side: (x + 14)(x + 14) = 236 Calculate the square root of the right side: 15.362291496 Break this problem into two subproblems by setting (x + 14) equal to 15.362291496 and -15.362291496.Subproblem 1
x + 14 = 15.362291496 Simplifying x + 14 = 15.362291496 Reorder the terms: 14 + x = 15.362291496 Solving 14 + x = 15.362291496 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 = 15.362291496 + -14 Combine like terms: 14 + -14 = 0 0 + x = 15.362291496 + -14 x = 15.362291496 + -14 Combine like terms: 15.362291496 + -14 = 1.362291496 x = 1.362291496 Simplifying x = 1.362291496Subproblem 2
x + 14 = -15.362291496 Simplifying x + 14 = -15.362291496 Reorder the terms: 14 + x = -15.362291496 Solving 14 + x = -15.362291496 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 = -15.362291496 + -14 Combine like terms: 14 + -14 = 0 0 + x = -15.362291496 + -14 x = -15.362291496 + -14 Combine like terms: -15.362291496 + -14 = -29.362291496 x = -29.362291496 Simplifying x = -29.362291496Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.362291496, -29.362291496}
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