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Simplifying 8x + 47 = 8x(x + 5) Reorder the terms: 47 + 8x = 8x(x + 5) Reorder the terms: 47 + 8x = 8x(5 + x) 47 + 8x = (5 * 8x + x * 8x) 47 + 8x = (40x + 8x2) Solving 47 + 8x = 40x + 8x2 Solving for variable 'x'. Combine like terms: 8x + -40x = -32x 47 + -32x + -8x2 = 40x + 8x2 + -40x + -8x2 Reorder the terms: 47 + -32x + -8x2 = 40x + -40x + 8x2 + -8x2 Combine like terms: 40x + -40x = 0 47 + -32x + -8x2 = 0 + 8x2 + -8x2 47 + -32x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 47 + -32x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -5.875 + 4x + x2 = 0 Move the constant term to the right: Add '5.875' to each side of the equation. -5.875 + 4x + 5.875 + x2 = 0 + 5.875 Reorder the terms: -5.875 + 5.875 + 4x + x2 = 0 + 5.875 Combine like terms: -5.875 + 5.875 = 0.000 0.000 + 4x + x2 = 0 + 5.875 4x + x2 = 0 + 5.875 Combine like terms: 0 + 5.875 = 5.875 4x + x2 = 5.875 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 5.875 + 4 Reorder the terms: 4 + 4x + x2 = 5.875 + 4 Combine like terms: 5.875 + 4 = 9.875 4 + 4x + x2 = 9.875 Factor a perfect square on the left side: (x + 2)(x + 2) = 9.875 Calculate the square root of the right side: 3.142451272 Break this problem into two subproblems by setting (x + 2) equal to 3.142451272 and -3.142451272.Subproblem 1
x + 2 = 3.142451272 Simplifying x + 2 = 3.142451272 Reorder the terms: 2 + x = 3.142451272 Solving 2 + x = 3.142451272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.142451272 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.142451272 + -2 x = 3.142451272 + -2 Combine like terms: 3.142451272 + -2 = 1.142451272 x = 1.142451272 Simplifying x = 1.142451272Subproblem 2
x + 2 = -3.142451272 Simplifying x + 2 = -3.142451272 Reorder the terms: 2 + x = -3.142451272 Solving 2 + x = -3.142451272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.142451272 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.142451272 + -2 x = -3.142451272 + -2 Combine like terms: -3.142451272 + -2 = -5.142451272 x = -5.142451272 Simplifying x = -5.142451272Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.142451272, -5.142451272}
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