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Simplifying 3x = 5x(x + 3) + -3 Reorder the terms: 3x = 5x(3 + x) + -3 3x = (3 * 5x + x * 5x) + -3 3x = (15x + 5x2) + -3 Reorder the terms: 3x = -3 + 15x + 5x2 Solving 3x = -3 + 15x + 5x2 Solving for variable 'x'. Reorder the terms: 3 + 3x + -15x + -5x2 = -3 + 15x + 5x2 + 3 + -15x + -5x2 Combine like terms: 3x + -15x = -12x 3 + -12x + -5x2 = -3 + 15x + 5x2 + 3 + -15x + -5x2 Reorder the terms: 3 + -12x + -5x2 = -3 + 3 + 15x + -15x + 5x2 + -5x2 Combine like terms: -3 + 3 = 0 3 + -12x + -5x2 = 0 + 15x + -15x + 5x2 + -5x2 3 + -12x + -5x2 = 15x + -15x + 5x2 + -5x2 Combine like terms: 15x + -15x = 0 3 + -12x + -5x2 = 0 + 5x2 + -5x2 3 + -12x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 3 + -12x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.6 + 2.4x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 2.4x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 2.4x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 2.4x + x2 = 0 + 0.6 2.4x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 2.4x + x2 = 0.6 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 0.6 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 0.6 + 1.44 Combine like terms: 0.6 + 1.44 = 2.04 1.44 + 2.4x + x2 = 2.04 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 2.04 Calculate the square root of the right side: 1.428285686 Break this problem into two subproblems by setting (x + 1.2) equal to 1.428285686 and -1.428285686.Subproblem 1
x + 1.2 = 1.428285686 Simplifying x + 1.2 = 1.428285686 Reorder the terms: 1.2 + x = 1.428285686 Solving 1.2 + x = 1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 1.428285686 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.428285686 + -1.2 x = 1.428285686 + -1.2 Combine like terms: 1.428285686 + -1.2 = 0.228285686 x = 0.228285686 Simplifying x = 0.228285686Subproblem 2
x + 1.2 = -1.428285686 Simplifying x + 1.2 = -1.428285686 Reorder the terms: 1.2 + x = -1.428285686 Solving 1.2 + x = -1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -1.428285686 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.428285686 + -1.2 x = -1.428285686 + -1.2 Combine like terms: -1.428285686 + -1.2 = -2.628285686 x = -2.628285686 Simplifying x = -2.628285686Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.228285686, -2.628285686}
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