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Simplifying 5(x + 5) * 3x = 13 Reorder the terms: 5(5 + x) * 3x = 13 Reorder the terms for easier multiplication: 5 * 3x(5 + x) = 13 Multiply 5 * 3 15x(5 + x) = 13 (5 * 15x + x * 15x) = 13 (75x + 15x2) = 13 Solving 75x + 15x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 75x + 15x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 75x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.8666666667 + 5x + x2 = 0 Move the constant term to the right: Add '0.8666666667' to each side of the equation. -0.8666666667 + 5x + 0.8666666667 + x2 = 0 + 0.8666666667 Reorder the terms: -0.8666666667 + 0.8666666667 + 5x + x2 = 0 + 0.8666666667 Combine like terms: -0.8666666667 + 0.8666666667 = 0.0000000000 0.0000000000 + 5x + x2 = 0 + 0.8666666667 5x + x2 = 0 + 0.8666666667 Combine like terms: 0 + 0.8666666667 = 0.8666666667 5x + x2 = 0.8666666667 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 0.8666666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 0.8666666667 + 6.25 Combine like terms: 0.8666666667 + 6.25 = 7.1166666667 6.25 + 5x + x2 = 7.1166666667 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 7.1166666667 Calculate the square root of the right side: 2.66770813 Break this problem into two subproblems by setting (x + 2.5) equal to 2.66770813 and -2.66770813.Subproblem 1
x + 2.5 = 2.66770813 Simplifying x + 2.5 = 2.66770813 Reorder the terms: 2.5 + x = 2.66770813 Solving 2.5 + x = 2.66770813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.66770813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.66770813 + -2.5 x = 2.66770813 + -2.5 Combine like terms: 2.66770813 + -2.5 = 0.16770813 x = 0.16770813 Simplifying x = 0.16770813Subproblem 2
x + 2.5 = -2.66770813 Simplifying x + 2.5 = -2.66770813 Reorder the terms: 2.5 + x = -2.66770813 Solving 2.5 + x = -2.66770813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.66770813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.66770813 + -2.5 x = -2.66770813 + -2.5 Combine like terms: -2.66770813 + -2.5 = -5.16770813 x = -5.16770813 Simplifying x = -5.16770813Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.16770813, -5.16770813}
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