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Simplifying 5(x2) + -16x = 96 Reorder the terms: -16x + 5x2 = 96 Solving -16x + 5x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + -16x + 5x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + -16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -19.2 + -3.2x + x2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + -3.2x + 19.2 + x2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + -3.2x + x2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + -3.2x + x2 = 0 + 19.2 -3.2x + x2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 -3.2x + x2 = 19.2 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 19.2 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 19.2 + 2.56 Combine like terms: 19.2 + 2.56 = 21.76 2.56 + -3.2x + x2 = 21.76 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 21.76 Calculate the square root of the right side: 4.664761516 Break this problem into two subproblems by setting (x + -1.6) equal to 4.664761516 and -4.664761516.Subproblem 1
x + -1.6 = 4.664761516 Simplifying x + -1.6 = 4.664761516 Reorder the terms: -1.6 + x = 4.664761516 Solving -1.6 + x = 4.664761516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 4.664761516 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 4.664761516 + 1.6 x = 4.664761516 + 1.6 Combine like terms: 4.664761516 + 1.6 = 6.264761516 x = 6.264761516 Simplifying x = 6.264761516Subproblem 2
x + -1.6 = -4.664761516 Simplifying x + -1.6 = -4.664761516 Reorder the terms: -1.6 + x = -4.664761516 Solving -1.6 + x = -4.664761516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -4.664761516 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -4.664761516 + 1.6 x = -4.664761516 + 1.6 Combine like terms: -4.664761516 + 1.6 = -3.064761516 x = -3.064761516 Simplifying x = -3.064761516Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.264761516, -3.064761516}
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