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Simplifying 50x2 + 16x + -64000 = 0 Reorder the terms: -64000 + 16x + 50x2 = 0 Solving -64000 + 16x + 50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-32000 + 8x + 25x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32000 + 8x + 25x2)' equal to zero and attempt to solve: Simplifying -32000 + 8x + 25x2 = 0 Solving -32000 + 8x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1280 + 0.32x + x2 = 0 Move the constant term to the right: Add '1280' to each side of the equation. -1280 + 0.32x + 1280 + x2 = 0 + 1280 Reorder the terms: -1280 + 1280 + 0.32x + x2 = 0 + 1280 Combine like terms: -1280 + 1280 = 0 0 + 0.32x + x2 = 0 + 1280 0.32x + x2 = 0 + 1280 Combine like terms: 0 + 1280 = 1280 0.32x + x2 = 1280 The x term is 0.32x. Take half its coefficient (0.16). Square it (0.0256) and add it to both sides. Add '0.0256' to each side of the equation. 0.32x + 0.0256 + x2 = 1280 + 0.0256 Reorder the terms: 0.0256 + 0.32x + x2 = 1280 + 0.0256 Combine like terms: 1280 + 0.0256 = 1280.0256 0.0256 + 0.32x + x2 = 1280.0256 Factor a perfect square on the left side: (x + 0.16)(x + 0.16) = 1280.0256 Calculate the square root of the right side: 35.777445409 Break this problem into two subproblems by setting (x + 0.16) equal to 35.777445409 and -35.777445409.Subproblem 1
x + 0.16 = 35.777445409 Simplifying x + 0.16 = 35.777445409 Reorder the terms: 0.16 + x = 35.777445409 Solving 0.16 + x = 35.777445409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.16' to each side of the equation. 0.16 + -0.16 + x = 35.777445409 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + x = 35.777445409 + -0.16 x = 35.777445409 + -0.16 Combine like terms: 35.777445409 + -0.16 = 35.617445409 x = 35.617445409 Simplifying x = 35.617445409Subproblem 2
x + 0.16 = -35.777445409 Simplifying x + 0.16 = -35.777445409 Reorder the terms: 0.16 + x = -35.777445409 Solving 0.16 + x = -35.777445409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.16' to each side of the equation. 0.16 + -0.16 + x = -35.777445409 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + x = -35.777445409 + -0.16 x = -35.777445409 + -0.16 Combine like terms: -35.777445409 + -0.16 = -35.937445409 x = -35.937445409 Simplifying x = -35.937445409Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.617445409, -35.937445409}Solution
x = {35.617445409, -35.937445409}
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