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Simplifying 0 = 2x2 + 12x + 13 Reorder the terms: 0 = 13 + 12x + 2x2 Solving 0 = 13 + 12x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -13 = -13 -13 + -12x + -2x2 = 13 + 12x + 2x2 + -13 + -12x + -2x2 Reorder the terms: -13 + -12x + -2x2 = 13 + -13 + 12x + -12x + 2x2 + -2x2 Combine like terms: 13 + -13 = 0 -13 + -12x + -2x2 = 0 + 12x + -12x + 2x2 + -2x2 -13 + -12x + -2x2 = 12x + -12x + 2x2 + -2x2 Combine like terms: 12x + -12x = 0 -13 + -12x + -2x2 = 0 + 2x2 + -2x2 -13 + -12x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -13 + -12x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 12x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 12x + 2x2)' equal to zero and attempt to solve: Simplifying 13 + 12x + 2x2 = 0 Solving 13 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + 6x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + 6x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + 6x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + 6x + x2 = 0 + -6.5 6x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 6x + x2 = -6.5 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 = -6.5 + 9 Reorder the terms: 9 + 6x + x2 = -6.5 + 9 Combine like terms: -6.5 + 9 = 2.5 9 + 6x + x2 = 2.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (x + 3) equal to 1.58113883 and -1.58113883.Subproblem 1
x + 3 = 1.58113883 Simplifying x + 3 = 1.58113883 Reorder the terms: 3 + x = 1.58113883 Solving 3 + x = 1.58113883 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 = 1.58113883 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.58113883 + -3 x = 1.58113883 + -3 Combine like terms: 1.58113883 + -3 = -1.41886117 x = -1.41886117 Simplifying x = -1.41886117Subproblem 2
x + 3 = -1.58113883 Simplifying x + 3 = -1.58113883 Reorder the terms: 3 + x = -1.58113883 Solving 3 + x = -1.58113883 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 = -1.58113883 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.58113883 + -3 x = -1.58113883 + -3 Combine like terms: -1.58113883 + -3 = -4.58113883 x = -4.58113883 Simplifying x = -4.58113883Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.41886117, -4.58113883}Solution
x = {-1.41886117, -4.58113883}
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