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Simplifying 4x2 + 32x + 57 = 0 Reorder the terms: 57 + 32x + 4x2 = 0 Solving 57 + 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'. 14.25 + 8x + x2 = 0 Move the constant term to the right: Add '-14.25' to each side of the equation. 14.25 + 8x + -14.25 + x2 = 0 + -14.25 Reorder the terms: 14.25 + -14.25 + 8x + x2 = 0 + -14.25 Combine like terms: 14.25 + -14.25 = 0.00 0.00 + 8x + x2 = 0 + -14.25 8x + x2 = 0 + -14.25 Combine like terms: 0 + -14.25 = -14.25 8x + x2 = -14.25 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 = -14.25 + 16 Reorder the terms: 16 + 8x + x2 = -14.25 + 16 Combine like terms: -14.25 + 16 = 1.75 16 + 8x + x2 = 1.75 Factor a perfect square on the left side: (x + 4)(x + 4) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + 4) equal to 1.322875656 and -1.322875656.Subproblem 1
x + 4 = 1.322875656 Simplifying x + 4 = 1.322875656 Reorder the terms: 4 + x = 1.322875656 Solving 4 + x = 1.322875656 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 = 1.322875656 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.322875656 + -4 x = 1.322875656 + -4 Combine like terms: 1.322875656 + -4 = -2.677124344 x = -2.677124344 Simplifying x = -2.677124344Subproblem 2
x + 4 = -1.322875656 Simplifying x + 4 = -1.322875656 Reorder the terms: 4 + x = -1.322875656 Solving 4 + x = -1.322875656 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 = -1.322875656 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.322875656 + -4 x = -1.322875656 + -4 Combine like terms: -1.322875656 + -4 = -5.322875656 x = -5.322875656 Simplifying x = -5.322875656Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.677124344, -5.322875656}
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