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Simplifying 4x2 + 32x + 23 = 0 Reorder the terms: 23 + 32x + 4x2 = 0 Solving 23 + 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'. 5.75 + 8x + x2 = 0 Move the constant term to the right: Add '-5.75' to each side of the equation. 5.75 + 8x + -5.75 + x2 = 0 + -5.75 Reorder the terms: 5.75 + -5.75 + 8x + x2 = 0 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + 8x + x2 = 0 + -5.75 8x + x2 = 0 + -5.75 Combine like terms: 0 + -5.75 = -5.75 8x + x2 = -5.75 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 = -5.75 + 16 Reorder the terms: 16 + 8x + x2 = -5.75 + 16 Combine like terms: -5.75 + 16 = 10.25 16 + 8x + x2 = 10.25 Factor a perfect square on the left side: (x + 4)(x + 4) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + 4) equal to 3.201562119 and -3.201562119.Subproblem 1
x + 4 = 3.201562119 Simplifying x + 4 = 3.201562119 Reorder the terms: 4 + x = 3.201562119 Solving 4 + x = 3.201562119 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 = 3.201562119 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.201562119 + -4 x = 3.201562119 + -4 Combine like terms: 3.201562119 + -4 = -0.798437881 x = -0.798437881 Simplifying x = -0.798437881Subproblem 2
x + 4 = -3.201562119 Simplifying x + 4 = -3.201562119 Reorder the terms: 4 + x = -3.201562119 Solving 4 + x = -3.201562119 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 = -3.201562119 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.201562119 + -4 x = -3.201562119 + -4 Combine like terms: -3.201562119 + -4 = -7.201562119 x = -7.201562119 Simplifying x = -7.201562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.798437881, -7.201562119}
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