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Simplifying -2x2 + 12x + 42 = 0 Reorder the terms: 42 + 12x + -2x2 = 0 Solving 42 + 12x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 6x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying 21 + 6x + -1x2 = 0 Solving 21 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + -6x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -6x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -6x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -6x + x2 = 0 + 21 -6x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -6x + x2 = 21 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 = 21 + 9 Reorder the terms: 9 + -6x + x2 = 21 + 9 Combine like terms: 21 + 9 = 30 9 + -6x + x2 = 30 Factor a perfect square on the left side: (x + -3)(x + -3) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + -3) equal to 5.477225575 and -5.477225575.Subproblem 1
x + -3 = 5.477225575 Simplifying x + -3 = 5.477225575 Reorder the terms: -3 + x = 5.477225575 Solving -3 + x = 5.477225575 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 = 5.477225575 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.477225575 + 3 x = 5.477225575 + 3 Combine like terms: 5.477225575 + 3 = 8.477225575 x = 8.477225575 Simplifying x = 8.477225575Subproblem 2
x + -3 = -5.477225575 Simplifying x + -3 = -5.477225575 Reorder the terms: -3 + x = -5.477225575 Solving -3 + x = -5.477225575 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 = -5.477225575 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.477225575 + 3 x = -5.477225575 + 3 Combine like terms: -5.477225575 + 3 = -2.477225575 x = -2.477225575 Simplifying x = -2.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.477225575, -2.477225575}Solution
x = {8.477225575, -2.477225575}
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