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Simplifying 7x(x + 3) + 5 = 3x(x + 2) Reorder the terms: 7x(3 + x) + 5 = 3x(x + 2) (3 * 7x + x * 7x) + 5 = 3x(x + 2) (21x + 7x2) + 5 = 3x(x + 2) Reorder the terms: 5 + 21x + 7x2 = 3x(x + 2) Reorder the terms: 5 + 21x + 7x2 = 3x(2 + x) 5 + 21x + 7x2 = (2 * 3x + x * 3x) 5 + 21x + 7x2 = (6x + 3x2) Solving 5 + 21x + 7x2 = 6x + 3x2 Solving for variable 'x'. Reorder the terms: 5 + 21x + -6x + 7x2 + -3x2 = 6x + 3x2 + -6x + -3x2 Combine like terms: 21x + -6x = 15x 5 + 15x + 7x2 + -3x2 = 6x + 3x2 + -6x + -3x2 Combine like terms: 7x2 + -3x2 = 4x2 5 + 15x + 4x2 = 6x + 3x2 + -6x + -3x2 Reorder the terms: 5 + 15x + 4x2 = 6x + -6x + 3x2 + -3x2 Combine like terms: 6x + -6x = 0 5 + 15x + 4x2 = 0 + 3x2 + -3x2 5 + 15x + 4x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 5 + 15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 3.75x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 3.75x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 3.75x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 3.75x + x2 = 0 + -1.25 3.75x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 3.75x + x2 = -1.25 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = -1.25 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = -1.25 + 3.515625 Combine like terms: -1.25 + 3.515625 = 2.265625 3.515625 + 3.75x + x2 = 2.265625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + 1.875) equal to 1.505199322 and -1.505199322.Subproblem 1
x + 1.875 = 1.505199322 Simplifying x + 1.875 = 1.505199322 Reorder the terms: 1.875 + x = 1.505199322 Solving 1.875 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 1.505199322 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 1.505199322 + -1.875 x = 1.505199322 + -1.875 Combine like terms: 1.505199322 + -1.875 = -0.369800678 x = -0.369800678 Simplifying x = -0.369800678Subproblem 2
x + 1.875 = -1.505199322 Simplifying x + 1.875 = -1.505199322 Reorder the terms: 1.875 + x = -1.505199322 Solving 1.875 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -1.505199322 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -1.505199322 + -1.875 x = -1.505199322 + -1.875 Combine like terms: -1.505199322 + -1.875 = -3.380199322 x = -3.380199322 Simplifying x = -3.380199322Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.369800678, -3.380199322}
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