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Simplifying 4x2 + 80x = 216 Reorder the terms: 80x + 4x2 = 216 Solving 80x + 4x2 = 216 Solving for variable 'x'. Reorder the terms: -216 + 80x + 4x2 = 216 + -216 Combine like terms: 216 + -216 = 0 -216 + 80x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-54 + 20x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-54 + 20x + x2)' equal to zero and attempt to solve: Simplifying -54 + 20x + x2 = 0 Solving -54 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 20x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 20x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 20x + x2 = 0 + 54 20x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 20x + x2 = 54 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 54 + 100 Reorder the terms: 100 + 20x + x2 = 54 + 100 Combine like terms: 54 + 100 = 154 100 + 20x + x2 = 154 Factor a perfect square on the left side: (x + 10)(x + 10) = 154 Calculate the square root of the right side: 12.409673646 Break this problem into two subproblems by setting (x + 10) equal to 12.409673646 and -12.409673646.Subproblem 1
x + 10 = 12.409673646 Simplifying x + 10 = 12.409673646 Reorder the terms: 10 + x = 12.409673646 Solving 10 + x = 12.409673646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 12.409673646 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.409673646 + -10 x = 12.409673646 + -10 Combine like terms: 12.409673646 + -10 = 2.409673646 x = 2.409673646 Simplifying x = 2.409673646Subproblem 2
x + 10 = -12.409673646 Simplifying x + 10 = -12.409673646 Reorder the terms: 10 + x = -12.409673646 Solving 10 + x = -12.409673646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -12.409673646 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.409673646 + -10 x = -12.409673646 + -10 Combine like terms: -12.409673646 + -10 = -22.409673646 x = -22.409673646 Simplifying x = -22.409673646Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.409673646, -22.409673646}Solution
x = {2.409673646, -22.409673646}
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