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Simplifying -1x2 + 16x + -40 = 0 Reorder the terms: -40 + 16x + -1x2 = 0 Solving -40 + 16x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 40 + -16x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -16x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -16x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -16x + x2 = 0 + -40 -16x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -16x + x2 = -40 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -40 + 64 Reorder the terms: 64 + -16x + x2 = -40 + 64 Combine like terms: -40 + 64 = 24 64 + -16x + x2 = 24 Factor a perfect square on the left side: (x + -8)(x + -8) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -8) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -8 = 4.898979486 Simplifying x + -8 = 4.898979486 Reorder the terms: -8 + x = 4.898979486 Solving -8 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 4.898979486 + 8 Combine like terms: -8 + 8 = 0 0 + x = 4.898979486 + 8 x = 4.898979486 + 8 Combine like terms: 4.898979486 + 8 = 12.898979486 x = 12.898979486 Simplifying x = 12.898979486Subproblem 2
x + -8 = -4.898979486 Simplifying x + -8 = -4.898979486 Reorder the terms: -8 + x = -4.898979486 Solving -8 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -4.898979486 + 8 Combine like terms: -8 + 8 = 0 0 + x = -4.898979486 + 8 x = -4.898979486 + 8 Combine like terms: -4.898979486 + 8 = 3.101020514 x = 3.101020514 Simplifying x = 3.101020514Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.898979486, 3.101020514}
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