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Simplifying -2x2 + 12x + 100 = 0 Reorder the terms: 100 + 12x + -2x2 = 0 Solving 100 + 12x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(50 + 6x + -1x2) = 0 Ignore the factor 2.Subproblem 1
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 = 10.681145748 x = 10.681145748 Simplifying x = 10.681145748Subproblem 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 = -4.681145748 x = -4.681145748 Simplifying x = -4.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.681145748, -4.681145748}Solution
x = {10.681145748, -4.681145748}
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