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Simplifying 15x(x + 2) = 13 + 15x Reorder the terms: 15x(2 + x) = 13 + 15x (2 * 15x + x * 15x) = 13 + 15x (30x + 15x2) = 13 + 15x Solving 30x + 15x2 = 13 + 15x Solving for variable 'x'. Reorder the terms: -13 + 30x + -15x + 15x2 = 13 + 15x + -13 + -15x Combine like terms: 30x + -15x = 15x -13 + 15x + 15x2 = 13 + 15x + -13 + -15x Reorder the terms: -13 + 15x + 15x2 = 13 + -13 + 15x + -15x Combine like terms: 13 + -13 = 0 -13 + 15x + 15x2 = 0 + 15x + -15x -13 + 15x + 15x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -13 + 15x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.8666666667 + x + x2 = 0 Move the constant term to the right: Add '0.8666666667' to each side of the equation. -0.8666666667 + x + 0.8666666667 + x2 = 0 + 0.8666666667 Reorder the terms: -0.8666666667 + 0.8666666667 + x + x2 = 0 + 0.8666666667 Combine like terms: -0.8666666667 + 0.8666666667 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.8666666667 x + x2 = 0 + 0.8666666667 Combine like terms: 0 + 0.8666666667 = 0.8666666667 x + x2 = 0.8666666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.8666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.8666666667 + 0.25 Combine like terms: 0.8666666667 + 0.25 = 1.1166666667 1.25 + x2 = 1.1166666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.1166666667 Calculate the square root of the right side: 1.056724499 Break this problem into two subproblems by setting (x + 0.5) equal to 1.056724499 and -1.056724499.Subproblem 1
x + 0.5 = 1.056724499 Simplifying x + 0.5 = 1.056724499 Reorder the terms: 0.5 + x = 1.056724499 Solving 0.5 + x = 1.056724499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.056724499 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.056724499 + -0.5 x = 1.056724499 + -0.5 Combine like terms: 1.056724499 + -0.5 = 0.556724499 x = 0.556724499 Simplifying x = 0.556724499Subproblem 2
x + 0.5 = -1.056724499 Simplifying x + 0.5 = -1.056724499 Reorder the terms: 0.5 + x = -1.056724499 Solving 0.5 + x = -1.056724499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.056724499 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.056724499 + -0.5 x = -1.056724499 + -0.5 Combine like terms: -1.056724499 + -0.5 = -1.556724499 x = -1.556724499 Simplifying x = -1.556724499Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.556724499, -1.556724499}
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