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Simplifying 4x2 + 32x + 9 = 0 Reorder the terms: 9 + 32x + 4x2 = 0 Solving 9 + 32x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 8x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 8x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 8x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 8x + x2 = 0 + -2.25 8x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 8x + x2 = -2.25 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 = -2.25 + 16 Reorder the terms: 16 + 8x + x2 = -2.25 + 16 Combine like terms: -2.25 + 16 = 13.75 16 + 8x + x2 = 13.75 Factor a perfect square on the left side: (x + 4)(x + 4) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (x + 4) equal to 3.708099244 and -3.708099244.Subproblem 1
x + 4 = 3.708099244 Simplifying x + 4 = 3.708099244 Reorder the terms: 4 + x = 3.708099244 Solving 4 + x = 3.708099244 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 = 3.708099244 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.708099244 + -4 x = 3.708099244 + -4 Combine like terms: 3.708099244 + -4 = -0.291900756 x = -0.291900756 Simplifying x = -0.291900756Subproblem 2
x + 4 = -3.708099244 Simplifying x + 4 = -3.708099244 Reorder the terms: 4 + x = -3.708099244 Solving 4 + x = -3.708099244 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 = -3.708099244 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.708099244 + -4 x = -3.708099244 + -4 Combine like terms: -3.708099244 + -4 = -7.708099244 x = -7.708099244 Simplifying x = -7.708099244Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.291900756, -7.708099244}
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