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Simplifying 2x + -12x2 + 32 = 0 Reorder the terms: 32 + 2x + -12x2 = 0 Solving 32 + 2x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + x + -6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + x + -6x2)' equal to zero and attempt to solve: Simplifying 16 + x + -6x2 = 0 Solving 16 + x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -2.666666667 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -0.1666666667x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -0.1666666667x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -0.1666666667x + x2 = 0 + 2.666666667 -0.1666666667x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -0.1666666667x + x2 = 2.666666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1666666667x + 0.25 + x2 = 2.666666667 + 0.25 Reorder the terms: 0.25 + -0.1666666667x + x2 = 2.666666667 + 0.25 Combine like terms: 2.666666667 + 0.25 = 2.916666667 0.25 + -0.1666666667x + x2 = 2.916666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.916666667 Calculate the square root of the right side: 1.707825128 Break this problem into two subproblems by setting (x + 0.5) equal to 1.707825128 and -1.707825128.Subproblem 1
x + 0.5 = 1.707825128 Simplifying x + 0.5 = 1.707825128 Reorder the terms: 0.5 + x = 1.707825128 Solving 0.5 + x = 1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.707825128 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.707825128 + -0.5 x = 1.707825128 + -0.5 Combine like terms: 1.707825128 + -0.5 = 1.207825128 x = 1.207825128 Simplifying x = 1.207825128Subproblem 2
x + 0.5 = -1.707825128 Simplifying x + 0.5 = -1.707825128 Reorder the terms: 0.5 + x = -1.707825128 Solving 0.5 + x = -1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.707825128 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.707825128 + -0.5 x = -1.707825128 + -0.5 Combine like terms: -1.707825128 + -0.5 = -2.207825128 x = -2.207825128 Simplifying x = -2.207825128Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.207825128, -2.207825128}Solution
x = {1.207825128, -2.207825128}
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