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Simplifying 100x + -2x3 = 12x2 Solving 100x + -2x3 = 12x2 Solving for variable 'x'. Reorder the terms: 100x + -12x2 + -2x3 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 100x + -12x2 + -2x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(50 + -6x + -1x2) = 0 Ignore the factor 2.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 '(50 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 50 + -6x + -1x2 = 0 Solving 50 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + 6x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 6x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 6x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 6x + x2 = 0 + 50 6x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 6x + x2 = 50 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 50 + 9 Reorder the terms: 9 + 6x + x2 = 50 + 9 Combine like terms: 50 + 9 = 59 9 + 6x + x2 = 59 Factor a perfect square on the left side: (x + 3)(x + 3) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + 3) equal to 7.681145748 and -7.681145748.Subproblem 1
x + 3 = 7.681145748 Simplifying x + 3 = 7.681145748 Reorder the terms: 3 + x = 7.681145748 Solving 3 + x = 7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.681145748 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.681145748 + -3 x = 7.681145748 + -3 Combine like terms: 7.681145748 + -3 = 4.681145748 x = 4.681145748 Simplifying x = 4.681145748Subproblem 2
x + 3 = -7.681145748 Simplifying x + 3 = -7.681145748 Reorder the terms: 3 + x = -7.681145748 Solving 3 + x = -7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.681145748 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.681145748 + -3 x = -7.681145748 + -3 Combine like terms: -7.681145748 + -3 = -10.681145748 x = -10.681145748 Simplifying x = -10.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.681145748, -10.681145748}Solution
x = {0, 4.681145748, -10.681145748}
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