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Simplifying x(x)(x) + -10x(10x) + 24x = 0 Multiply x * x x2 * x + -10x(10x) + 24x = 0 Multiply x2 * x x3 + -10x(10x) + 24x = 0 Remove parenthesis around (10x) x3 + -10x * 10x + 24x = 0 Reorder the terms for easier multiplication: x3 + -10 * 10x * x + 24x = 0 Multiply -10 * 10 x3 + -100x * x + 24x = 0 Multiply x * x x3 + -100x2 + 24x = 0 Reorder the terms: 24x + -100x2 + x3 = 0 Solving 24x + -100x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(24 + -100x + x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(24 + -100x + x2)' equal to zero and attempt to solve: Simplifying 24 + -100x + x2 = 0 Solving 24 + -100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -100x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -100x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -100x + x2 = 0 + -24 -100x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -100x + x2 = -24 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 = -24 + 2500 Reorder the terms: 2500 + -100x + x2 = -24 + 2500 Combine like terms: -24 + 2500 = 2476 2500 + -100x + x2 = 2476 Factor a perfect square on the left side: (x + -50)(x + -50) = 2476 Calculate the square root of the right side: 49.759421218 Break this problem into two subproblems by setting (x + -50) equal to 49.759421218 and -49.759421218.Subproblem 1
x + -50 = 49.759421218 Simplifying x + -50 = 49.759421218 Reorder the terms: -50 + x = 49.759421218 Solving -50 + x = 49.759421218 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 = 49.759421218 + 50 Combine like terms: -50 + 50 = 0 0 + x = 49.759421218 + 50 x = 49.759421218 + 50 Combine like terms: 49.759421218 + 50 = 99.759421218 x = 99.759421218 Simplifying x = 99.759421218Subproblem 2
x + -50 = -49.759421218 Simplifying x + -50 = -49.759421218 Reorder the terms: -50 + x = -49.759421218 Solving -50 + x = -49.759421218 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 = -49.759421218 + 50 Combine like terms: -50 + 50 = 0 0 + x = -49.759421218 + 50 x = -49.759421218 + 50 Combine like terms: -49.759421218 + 50 = 0.240578782 x = 0.240578782 Simplifying x = 0.240578782Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.759421218, 0.240578782}Solution
x = {0, 99.759421218, 0.240578782}
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