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Simplifying 4x(x + 3) = 1 Reorder the terms: 4x(3 + x) = 1 (3 * 4x + x * 4x) = 1 (12x + 4x2) = 1 Solving 12x + 4x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 12x + 4x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 3x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 3x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 3x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 3x + x2 = 0 + 0.25 3x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 3x + x2 = 0.25 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 0.25 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.25 + 2.25 Combine like terms: 0.25 + 2.25 = 2.5 2.25 + 3x + x2 = 2.5 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (x + 1.5) equal to 1.58113883 and -1.58113883.Subproblem 1
x + 1.5 = 1.58113883 Simplifying x + 1.5 = 1.58113883 Reorder the terms: 1.5 + x = 1.58113883 Solving 1.5 + x = 1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.58113883 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.58113883 + -1.5 x = 1.58113883 + -1.5 Combine like terms: 1.58113883 + -1.5 = 0.08113883 x = 0.08113883 Simplifying x = 0.08113883Subproblem 2
x + 1.5 = -1.58113883 Simplifying x + 1.5 = -1.58113883 Reorder the terms: 1.5 + x = -1.58113883 Solving 1.5 + x = -1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.58113883 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.58113883 + -1.5 x = -1.58113883 + -1.5 Combine like terms: -1.58113883 + -1.5 = -3.08113883 x = -3.08113883 Simplifying x = -3.08113883Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.08113883, -3.08113883}
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