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Simplifying 96 + 40x + 4x2 = 3 Solving 96 + 40x + 4x2 = 3 Solving for variable 'x'. Reorder the terms: 96 + -3 + 40x + 4x2 = 3 + -3 Combine like terms: 96 + -3 = 93 93 + 40x + 4x2 = 3 + -3 Combine like terms: 3 + -3 = 0 93 + 40x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 23.25 + 10x + x2 = 0 Move the constant term to the right: Add '-23.25' to each side of the equation. 23.25 + 10x + -23.25 + x2 = 0 + -23.25 Reorder the terms: 23.25 + -23.25 + 10x + x2 = 0 + -23.25 Combine like terms: 23.25 + -23.25 = 0.00 0.00 + 10x + x2 = 0 + -23.25 10x + x2 = 0 + -23.25 Combine like terms: 0 + -23.25 = -23.25 10x + x2 = -23.25 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -23.25 + 25 Reorder the terms: 25 + 10x + x2 = -23.25 + 25 Combine like terms: -23.25 + 25 = 1.75 25 + 10x + x2 = 1.75 Factor a perfect square on the left side: (x + 5)(x + 5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + 5) equal to 1.322875656 and -1.322875656.Subproblem 1
x + 5 = 1.322875656 Simplifying x + 5 = 1.322875656 Reorder the terms: 5 + x = 1.322875656 Solving 5 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 1.322875656 + -5 Combine like terms: 5 + -5 = 0 0 + x = 1.322875656 + -5 x = 1.322875656 + -5 Combine like terms: 1.322875656 + -5 = -3.677124344 x = -3.677124344 Simplifying x = -3.677124344Subproblem 2
x + 5 = -1.322875656 Simplifying x + 5 = -1.322875656 Reorder the terms: 5 + x = -1.322875656 Solving 5 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -1.322875656 + -5 Combine like terms: 5 + -5 = 0 0 + x = -1.322875656 + -5 x = -1.322875656 + -5 Combine like terms: -1.322875656 + -5 = -6.322875656 x = -6.322875656 Simplifying x = -6.322875656Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.677124344, -6.322875656}
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