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Simplifying 50 = 0.5x(x + -8) Reorder the terms: 50 = 0.5x(-8 + x) 50 = (-8 * 0.5x + x * 0.5x) 50 = (-4x + 0.5x2) Solving 50 = -4x + 0.5x2 Solving for variable 'x'. Reorder the terms: 50 + 4x + -0.5x2 = -4x + 4x + 0.5x2 + -0.5x2 Combine like terms: -4x + 4x = 0 50 + 4x + -0.5x2 = 0 + 0.5x2 + -0.5x2 50 + 4x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 50 + 4x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -100 + -8x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -8x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -8x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -8x + x2 = 0 + 100 -8x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -8x + x2 = 100 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 100 + 16 Reorder the terms: 16 + -8x + x2 = 100 + 16 Combine like terms: 100 + 16 = 116 16 + -8x + x2 = 116 Factor a perfect square on the left side: (x + -4)(x + -4) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (x + -4) equal to 10.770329614 and -10.770329614.Subproblem 1
x + -4 = 10.770329614 Simplifying x + -4 = 10.770329614 Reorder the terms: -4 + x = 10.770329614 Solving -4 + x = 10.770329614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 10.770329614 + 4 Combine like terms: -4 + 4 = 0 0 + x = 10.770329614 + 4 x = 10.770329614 + 4 Combine like terms: 10.770329614 + 4 = 14.770329614 x = 14.770329614 Simplifying x = 14.770329614Subproblem 2
x + -4 = -10.770329614 Simplifying x + -4 = -10.770329614 Reorder the terms: -4 + x = -10.770329614 Solving -4 + x = -10.770329614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -10.770329614 + 4 Combine like terms: -4 + 4 = 0 0 + x = -10.770329614 + 4 x = -10.770329614 + 4 Combine like terms: -10.770329614 + 4 = -6.770329614 x = -6.770329614 Simplifying x = -6.770329614Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.770329614, -6.770329614}
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