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Simplifying 4x3 + -72x2 + 228x = 0 Reorder the terms: 228x + -72x2 + 4x3 = 0 Solving 228x + -72x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(57 + -18x + x2) = 0 Ignore the factor 4.Subproblem 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 '(57 + -18x + x2)' equal to zero and attempt to solve: Simplifying 57 + -18x + x2 = 0 Solving 57 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-57' to each side of the equation. 57 + -18x + -57 + x2 = 0 + -57 Reorder the terms: 57 + -57 + -18x + x2 = 0 + -57 Combine like terms: 57 + -57 = 0 0 + -18x + x2 = 0 + -57 -18x + x2 = 0 + -57 Combine like terms: 0 + -57 = -57 -18x + x2 = -57 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -57 + 81 Reorder the terms: 81 + -18x + x2 = -57 + 81 Combine like terms: -57 + 81 = 24 81 + -18x + x2 = 24 Factor a perfect square on the left side: (x + -9)(x + -9) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -9) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -9 = 4.898979486 Simplifying x + -9 = 4.898979486 Reorder the terms: -9 + x = 4.898979486 Solving -9 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 4.898979486 + 9 Combine like terms: -9 + 9 = 0 0 + x = 4.898979486 + 9 x = 4.898979486 + 9 Combine like terms: 4.898979486 + 9 = 13.898979486 x = 13.898979486 Simplifying x = 13.898979486Subproblem 2
x + -9 = -4.898979486 Simplifying x + -9 = -4.898979486 Reorder the terms: -9 + x = -4.898979486 Solving -9 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -4.898979486 + 9 Combine like terms: -9 + 9 = 0 0 + x = -4.898979486 + 9 x = -4.898979486 + 9 Combine like terms: -4.898979486 + 9 = 4.101020514 x = 4.101020514 Simplifying x = 4.101020514Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.898979486, 4.101020514}Solution
x = {0, 13.898979486, 4.101020514}
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