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Simplifying 3(3x + 5) * x = 5 Reorder the terms: 3(5 + 3x) * x = 5 Reorder the terms for easier multiplication: 3x(5 + 3x) = 5 (5 * 3x + 3x * 3x) = 5 (15x + 9x2) = 5 Solving 15x + 9x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 15x + 9x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 15x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 1.666666667x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 1.666666667x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 1.666666667x + x2 = 0 + 0.5555555556 1.666666667x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 1.666666667x + x2 = 0.5555555556 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 0.5555555556 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 0.5555555556 + 0.6944444447 Combine like terms: 0.5555555556 + 0.6944444447 = 1.2500000003 0.6944444447 + 1.666666667x + x2 = 1.2500000003 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 1.2500000003 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 0.8333333335 = 1.118033989 Simplifying x + 0.8333333335 = 1.118033989 Reorder the terms: 0.8333333335 + x = 1.118033989 Solving 0.8333333335 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.118033989 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.118033989 + -0.8333333335 x = 1.118033989 + -0.8333333335 Combine like terms: 1.118033989 + -0.8333333335 = 0.2847006555 x = 0.2847006555 Simplifying x = 0.2847006555Subproblem 2
x + 0.8333333335 = -1.118033989 Simplifying x + 0.8333333335 = -1.118033989 Reorder the terms: 0.8333333335 + x = -1.118033989 Solving 0.8333333335 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.118033989 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.118033989 + -0.8333333335 x = -1.118033989 + -0.8333333335 Combine like terms: -1.118033989 + -0.8333333335 = -1.9513673225 x = -1.9513673225 Simplifying x = -1.9513673225Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2847006555, -1.9513673225}
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