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Simplifying 3x2 + -30x = 99 Reorder the terms: -30x + 3x2 = 99 Solving -30x + 3x2 = 99 Solving for variable 'x'. Reorder the terms: -99 + -30x + 3x2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + -30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-33 + -10x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-33 + -10x + x2)' equal to zero and attempt to solve: Simplifying -33 + -10x + x2 = 0 Solving -33 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -10x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + -10x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -10x + x2 = 0 + 33 -10x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 -10x + x2 = 33 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 33 + 25 Reorder the terms: 25 + -10x + x2 = 33 + 25 Combine like terms: 33 + 25 = 58 25 + -10x + x2 = 58 Factor a perfect square on the left side: (x + -5)(x + -5) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + -5) equal to 7.615773106 and -7.615773106.Subproblem 1
x + -5 = 7.615773106 Simplifying x + -5 = 7.615773106 Reorder the terms: -5 + x = 7.615773106 Solving -5 + x = 7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 7.615773106 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.615773106 + 5 x = 7.615773106 + 5 Combine like terms: 7.615773106 + 5 = 12.615773106 x = 12.615773106 Simplifying x = 12.615773106Subproblem 2
x + -5 = -7.615773106 Simplifying x + -5 = -7.615773106 Reorder the terms: -5 + x = -7.615773106 Solving -5 + x = -7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -7.615773106 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.615773106 + 5 x = -7.615773106 + 5 Combine like terms: -7.615773106 + 5 = -2.615773106 x = -2.615773106 Simplifying x = -2.615773106Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.615773106, -2.615773106}Solution
x = {12.615773106, -2.615773106}
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