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Simplifying 4x2 + 32x + -93 = 0 Reorder the terms: -93 + 32x + 4x2 = 0 Solving -93 + 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'. -23.25 + 8x + x2 = 0 Move the constant term to the right: Add '23.25' to each side of the equation. -23.25 + 8x + 23.25 + x2 = 0 + 23.25 Reorder the terms: -23.25 + 23.25 + 8x + x2 = 0 + 23.25 Combine like terms: -23.25 + 23.25 = 0.00 0.00 + 8x + x2 = 0 + 23.25 8x + x2 = 0 + 23.25 Combine like terms: 0 + 23.25 = 23.25 8x + x2 = 23.25 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 = 23.25 + 16 Reorder the terms: 16 + 8x + x2 = 23.25 + 16 Combine like terms: 23.25 + 16 = 39.25 16 + 8x + x2 = 39.25 Factor a perfect square on the left side: (x + 4)(x + 4) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + 4) equal to 6.264982043 and -6.264982043.Subproblem 1
x + 4 = 6.264982043 Simplifying x + 4 = 6.264982043 Reorder the terms: 4 + x = 6.264982043 Solving 4 + x = 6.264982043 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 = 6.264982043 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.264982043 + -4 x = 6.264982043 + -4 Combine like terms: 6.264982043 + -4 = 2.264982043 x = 2.264982043 Simplifying x = 2.264982043Subproblem 2
x + 4 = -6.264982043 Simplifying x + 4 = -6.264982043 Reorder the terms: 4 + x = -6.264982043 Solving 4 + x = -6.264982043 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 = -6.264982043 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.264982043 + -4 x = -6.264982043 + -4 Combine like terms: -6.264982043 + -4 = -10.264982043 x = -10.264982043 Simplifying x = -10.264982043Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.264982043, -10.264982043}
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