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Simplifying 2(x2 + 5) = 7x + 48 Reorder the terms: 2(5 + x2) = 7x + 48 (5 * 2 + x2 * 2) = 7x + 48 (10 + 2x2) = 7x + 48 Reorder the terms: 10 + 2x2 = 48 + 7x Solving 10 + 2x2 = 48 + 7x Solving for variable 'x'. Reorder the terms: 10 + -48 + -7x + 2x2 = 48 + 7x + -48 + -7x Combine like terms: 10 + -48 = -38 -38 + -7x + 2x2 = 48 + 7x + -48 + -7x Reorder the terms: -38 + -7x + 2x2 = 48 + -48 + 7x + -7x Combine like terms: 48 + -48 = 0 -38 + -7x + 2x2 = 0 + 7x + -7x -38 + -7x + 2x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -38 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19 + -3.5x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + -3.5x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -3.5x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -3.5x + x2 = 0 + 19 -3.5x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -3.5x + x2 = 19 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 19 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 19 + 3.0625 Combine like terms: 19 + 3.0625 = 22.0625 3.0625 + -3.5x + x2 = 22.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (x + -1.75) equal to 4.697073557 and -4.697073557.Subproblem 1
x + -1.75 = 4.697073557 Simplifying x + -1.75 = 4.697073557 Reorder the terms: -1.75 + x = 4.697073557 Solving -1.75 + x = 4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 4.697073557 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 4.697073557 + 1.75 x = 4.697073557 + 1.75 Combine like terms: 4.697073557 + 1.75 = 6.447073557 x = 6.447073557 Simplifying x = 6.447073557Subproblem 2
x + -1.75 = -4.697073557 Simplifying x + -1.75 = -4.697073557 Reorder the terms: -1.75 + x = -4.697073557 Solving -1.75 + x = -4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -4.697073557 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -4.697073557 + 1.75 x = -4.697073557 + 1.75 Combine like terms: -4.697073557 + 1.75 = -2.947073557 x = -2.947073557 Simplifying x = -2.947073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.447073557, -2.947073557}
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