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Simplifying 500 = -2x2 + 80x Reorder the terms: 500 = 80x + -2x2 Solving 500 = 80x + -2x2 Solving for variable 'x'. Reorder the terms: 500 + -80x + 2x2 = 80x + -80x + -2x2 + 2x2 Combine like terms: 80x + -80x = 0 500 + -80x + 2x2 = 0 + -2x2 + 2x2 500 + -80x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 500 + -80x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(250 + -40x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(250 + -40x + x2)' equal to zero and attempt to solve: Simplifying 250 + -40x + x2 = 0 Solving 250 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-250' to each side of the equation. 250 + -40x + -250 + x2 = 0 + -250 Reorder the terms: 250 + -250 + -40x + x2 = 0 + -250 Combine like terms: 250 + -250 = 0 0 + -40x + x2 = 0 + -250 -40x + x2 = 0 + -250 Combine like terms: 0 + -250 = -250 -40x + x2 = -250 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -250 + 400 Reorder the terms: 400 + -40x + x2 = -250 + 400 Combine like terms: -250 + 400 = 150 400 + -40x + x2 = 150 Factor a perfect square on the left side: (x + -20)(x + -20) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (x + -20) equal to 12.247448714 and -12.247448714.Subproblem 1
x + -20 = 12.247448714 Simplifying x + -20 = 12.247448714 Reorder the terms: -20 + x = 12.247448714 Solving -20 + x = 12.247448714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 12.247448714 + 20 Combine like terms: -20 + 20 = 0 0 + x = 12.247448714 + 20 x = 12.247448714 + 20 Combine like terms: 12.247448714 + 20 = 32.247448714 x = 32.247448714 Simplifying x = 32.247448714Subproblem 2
x + -20 = -12.247448714 Simplifying x + -20 = -12.247448714 Reorder the terms: -20 + x = -12.247448714 Solving -20 + x = -12.247448714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -12.247448714 + 20 Combine like terms: -20 + 20 = 0 0 + x = -12.247448714 + 20 x = -12.247448714 + 20 Combine like terms: -12.247448714 + 20 = 7.752551286 x = 7.752551286 Simplifying x = 7.752551286Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.247448714, 7.752551286}Solution
x = {32.247448714, 7.752551286}
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