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Simplifying 5 = 2x2 + 12x + -3 Reorder the terms: 5 = -3 + 12x + 2x2 Solving 5 = -3 + 12x + 2x2 Solving for variable 'x'. Combine like terms: 5 + 3 = 8 8 + -12x + -2x2 = -3 + 12x + 2x2 + 3 + -12x + -2x2 Reorder the terms: 8 + -12x + -2x2 = -3 + 3 + 12x + -12x + 2x2 + -2x2 Combine like terms: -3 + 3 = 0 8 + -12x + -2x2 = 0 + 12x + -12x + 2x2 + -2x2 8 + -12x + -2x2 = 12x + -12x + 2x2 + -2x2 Combine like terms: 12x + -12x = 0 8 + -12x + -2x2 = 0 + 2x2 + -2x2 8 + -12x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 8 + -12x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -6x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + -6x + -1x2 = 0 Solving 4 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 6x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 6x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 6x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6x + x2 = 0 + 4 6x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 6x + x2 = 4 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 = 4 + 9 Reorder the terms: 9 + 6x + x2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + 6x + x2 = 13 Factor a perfect square on the left side: (x + 3)(x + 3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 3) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 3 = 3.605551275 Simplifying x + 3 = 3.605551275 Reorder the terms: 3 + x = 3.605551275 Solving 3 + x = 3.605551275 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 = 3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.605551275 + -3 x = 3.605551275 + -3 Combine like terms: 3.605551275 + -3 = 0.605551275 x = 0.605551275 Simplifying x = 0.605551275Subproblem 2
x + 3 = -3.605551275 Simplifying x + 3 = -3.605551275 Reorder the terms: 3 + x = -3.605551275 Solving 3 + x = -3.605551275 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 = -3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.605551275 + -3 x = -3.605551275 + -3 Combine like terms: -3.605551275 + -3 = -6.605551275 x = -6.605551275 Simplifying x = -6.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.605551275, -6.605551275}Solution
x = {0.605551275, -6.605551275}
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