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Simplifying 5000 = 16x2 + 4686 + -10x Reorder the terms: 5000 = 4686 + -10x + 16x2 Solving 5000 = 4686 + -10x + 16x2 Solving for variable 'x'. Combine like terms: 5000 + -4686 = 314 314 + 10x + -16x2 = 4686 + -10x + 16x2 + -4686 + 10x + -16x2 Reorder the terms: 314 + 10x + -16x2 = 4686 + -4686 + -10x + 10x + 16x2 + -16x2 Combine like terms: 4686 + -4686 = 0 314 + 10x + -16x2 = 0 + -10x + 10x + 16x2 + -16x2 314 + 10x + -16x2 = -10x + 10x + 16x2 + -16x2 Combine like terms: -10x + 10x = 0 314 + 10x + -16x2 = 0 + 16x2 + -16x2 314 + 10x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 314 + 10x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(157 + 5x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(157 + 5x + -8x2)' equal to zero and attempt to solve: Simplifying 157 + 5x + -8x2 = 0 Solving 157 + 5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -19.625 + -0.625x + x2 = 0 Move the constant term to the right: Add '19.625' to each side of the equation. -19.625 + -0.625x + 19.625 + x2 = 0 + 19.625 Reorder the terms: -19.625 + 19.625 + -0.625x + x2 = 0 + 19.625 Combine like terms: -19.625 + 19.625 = 0.000 0.000 + -0.625x + x2 = 0 + 19.625 -0.625x + x2 = 0 + 19.625 Combine like terms: 0 + 19.625 = 19.625 -0.625x + x2 = 19.625 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 19.625 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 19.625 + 0.09765625 Combine like terms: 19.625 + 0.09765625 = 19.72265625 0.09765625 + -0.625x + x2 = 19.72265625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 19.72265625 Calculate the square root of the right side: 4.441019731 Break this problem into two subproblems by setting (x + -0.3125) equal to 4.441019731 and -4.441019731.Subproblem 1
x + -0.3125 = 4.441019731 Simplifying x + -0.3125 = 4.441019731 Reorder the terms: -0.3125 + x = 4.441019731 Solving -0.3125 + x = 4.441019731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 4.441019731 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 4.441019731 + 0.3125 x = 4.441019731 + 0.3125 Combine like terms: 4.441019731 + 0.3125 = 4.753519731 x = 4.753519731 Simplifying x = 4.753519731Subproblem 2
x + -0.3125 = -4.441019731 Simplifying x + -0.3125 = -4.441019731 Reorder the terms: -0.3125 + x = -4.441019731 Solving -0.3125 + x = -4.441019731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -4.441019731 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -4.441019731 + 0.3125 x = -4.441019731 + 0.3125 Combine like terms: -4.441019731 + 0.3125 = -4.128519731 x = -4.128519731 Simplifying x = -4.128519731Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.753519731, -4.128519731}Solution
x = {4.753519731, -4.128519731}
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