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Simplifying 2x2 + 16x = -3 Reorder the terms: 16x + 2x2 = -3 Solving 16x + 2x2 = -3 Solving for variable 'x'. Reorder the terms: 3 + 16x + 2x2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + 16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 8x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 8x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 8x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 8x + x2 = 0 + -1.5 8x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 8x + x2 = -1.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -1.5 + 16 Reorder the terms: 16 + 8x + x2 = -1.5 + 16 Combine like terms: -1.5 + 16 = 14.5 16 + 8x + x2 = 14.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (x + 4) equal to 3.807886553 and -3.807886553.Subproblem 1
x + 4 = 3.807886553 Simplifying x + 4 = 3.807886553 Reorder the terms: 4 + x = 3.807886553 Solving 4 + x = 3.807886553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.807886553 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.807886553 + -4 x = 3.807886553 + -4 Combine like terms: 3.807886553 + -4 = -0.192113447 x = -0.192113447 Simplifying x = -0.192113447Subproblem 2
x + 4 = -3.807886553 Simplifying x + 4 = -3.807886553 Reorder the terms: 4 + x = -3.807886553 Solving 4 + x = -3.807886553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.807886553 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.807886553 + -4 x = -3.807886553 + -4 Combine like terms: -3.807886553 + -4 = -7.807886553 x = -7.807886553 Simplifying x = -7.807886553Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.192113447, -7.807886553}
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