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Simplifying 8x(x + 100) + -3 = 837 Reorder the terms: 8x(100 + x) + -3 = 837 (100 * 8x + x * 8x) + -3 = 837 (800x + 8x2) + -3 = 837 Reorder the terms: -3 + 800x + 8x2 = 837 Solving -3 + 800x + 8x2 = 837 Solving for variable 'x'. Reorder the terms: -3 + -837 + 800x + 8x2 = 837 + -837 Combine like terms: -3 + -837 = -840 -840 + 800x + 8x2 = 837 + -837 Combine like terms: 837 + -837 = 0 -840 + 800x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-105 + 100x + x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-105 + 100x + x2)' equal to zero and attempt to solve: Simplifying -105 + 100x + x2 = 0 Solving -105 + 100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + 100x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + 100x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + 100x + x2 = 0 + 105 100x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 100x + x2 = 105 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 105 + 2500 Reorder the terms: 2500 + 100x + x2 = 105 + 2500 Combine like terms: 105 + 2500 = 2605 2500 + 100x + x2 = 2605 Factor a perfect square on the left side: (x + 50)(x + 50) = 2605 Calculate the square root of the right side: 51.039200621 Break this problem into two subproblems by setting (x + 50) equal to 51.039200621 and -51.039200621.Subproblem 1
x + 50 = 51.039200621 Simplifying x + 50 = 51.039200621 Reorder the terms: 50 + x = 51.039200621 Solving 50 + x = 51.039200621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 51.039200621 + -50 Combine like terms: 50 + -50 = 0 0 + x = 51.039200621 + -50 x = 51.039200621 + -50 Combine like terms: 51.039200621 + -50 = 1.039200621 x = 1.039200621 Simplifying x = 1.039200621Subproblem 2
x + 50 = -51.039200621 Simplifying x + 50 = -51.039200621 Reorder the terms: 50 + x = -51.039200621 Solving 50 + x = -51.039200621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -51.039200621 + -50 Combine like terms: 50 + -50 = 0 0 + x = -51.039200621 + -50 x = -51.039200621 + -50 Combine like terms: -51.039200621 + -50 = -101.039200621 x = -101.039200621 Simplifying x = -101.039200621Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.039200621, -101.039200621}Solution
x = {1.039200621, -101.039200621}
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