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Simplifying 0 = x2 + 100x + 1000 Reorder the terms: 0 = 1000 + 100x + x2 Solving 0 = 1000 + 100x + x2 Solving for variable 'x'. Combine like terms: 0 + -1000 = -1000 -1000 + -100x + -1x2 = 1000 + 100x + x2 + -1000 + -100x + -1x2 Reorder the terms: -1000 + -100x + -1x2 = 1000 + -1000 + 100x + -100x + x2 + -1x2 Combine like terms: 1000 + -1000 = 0 -1000 + -100x + -1x2 = 0 + 100x + -100x + x2 + -1x2 -1000 + -100x + -1x2 = 100x + -100x + x2 + -1x2 Combine like terms: 100x + -100x = 0 -1000 + -100x + -1x2 = 0 + x2 + -1x2 -1000 + -100x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1000 + -100x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1000 + 100x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1000 + 100x + x2)' equal to zero and attempt to solve: Simplifying 1000 + 100x + x2 = 0 Solving 1000 + 100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + 100x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + 100x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + 100x + x2 = 0 + -1000 100x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 100x + x2 = -1000 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 = -1000 + 2500 Reorder the terms: 2500 + 100x + x2 = -1000 + 2500 Combine like terms: -1000 + 2500 = 1500 2500 + 100x + x2 = 1500 Factor a perfect square on the left side: (x + 50)(x + 50) = 1500 Calculate the square root of the right side: 38.729833462 Break this problem into two subproblems by setting (x + 50) equal to 38.729833462 and -38.729833462.Subproblem 1
x + 50 = 38.729833462 Simplifying x + 50 = 38.729833462 Reorder the terms: 50 + x = 38.729833462 Solving 50 + x = 38.729833462 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 = 38.729833462 + -50 Combine like terms: 50 + -50 = 0 0 + x = 38.729833462 + -50 x = 38.729833462 + -50 Combine like terms: 38.729833462 + -50 = -11.270166538 x = -11.270166538 Simplifying x = -11.270166538Subproblem 2
x + 50 = -38.729833462 Simplifying x + 50 = -38.729833462 Reorder the terms: 50 + x = -38.729833462 Solving 50 + x = -38.729833462 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 = -38.729833462 + -50 Combine like terms: 50 + -50 = 0 0 + x = -38.729833462 + -50 x = -38.729833462 + -50 Combine like terms: -38.729833462 + -50 = -88.729833462 x = -88.729833462 Simplifying x = -88.729833462Solution
The solution to the problem is based on the solutions from the subproblems. x = {-11.270166538, -88.729833462}Solution
x = {-11.270166538, -88.729833462}
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