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Simplifying 3x(2x + 5) = 4 Reorder the terms: 3x(5 + 2x) = 4 (5 * 3x + 2x * 3x) = 4 (15x + 6x2) = 4 Solving 15x + 6x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 15x + 6x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 15x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.6666666667 + 2.5x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 2.5x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 2.5x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 2.5x + x2 = 0 + 0.6666666667 2.5x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 2.5x + x2 = 0.6666666667 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 0.6666666667 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 0.6666666667 + 1.5625 Combine like terms: 0.6666666667 + 1.5625 = 2.2291666667 1.5625 + 2.5x + x2 = 2.2291666667 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 2.2291666667 Calculate the square root of the right side: 1.493039406 Break this problem into two subproblems by setting (x + 1.25) equal to 1.493039406 and -1.493039406.Subproblem 1
x + 1.25 = 1.493039406 Simplifying x + 1.25 = 1.493039406 Reorder the terms: 1.25 + x = 1.493039406 Solving 1.25 + x = 1.493039406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.493039406 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.493039406 + -1.25 x = 1.493039406 + -1.25 Combine like terms: 1.493039406 + -1.25 = 0.243039406 x = 0.243039406 Simplifying x = 0.243039406Subproblem 2
x + 1.25 = -1.493039406 Simplifying x + 1.25 = -1.493039406 Reorder the terms: 1.25 + x = -1.493039406 Solving 1.25 + x = -1.493039406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.493039406 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.493039406 + -1.25 x = -1.493039406 + -1.25 Combine like terms: -1.493039406 + -1.25 = -2.743039406 x = -2.743039406 Simplifying x = -2.743039406Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.243039406, -2.743039406}
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