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Simplifying 2x + 3x(x + -5) = 15 Reorder the terms: 2x + 3x(-5 + x) = 15 2x + (-5 * 3x + x * 3x) = 15 2x + (-15x + 3x2) = 15 Combine like terms: 2x + -15x = -13x -13x + 3x2 = 15 Solving -13x + 3x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -13x + 3x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + -4.333333333x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -4.333333333x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -4.333333333x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4.333333333x + x2 = 0 + 5 -4.333333333x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4.333333333x + x2 = 5 The x term is -4.333333333x. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333x + 4.694444446 + x2 = 5 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333x + x2 = 5 + 4.694444446 Combine like terms: 5 + 4.694444446 = 9.694444446 4.694444446 + -4.333333333x + x2 = 9.694444446 Factor a perfect square on the left side: (x + -2.166666667)(x + -2.166666667) = 9.694444446 Calculate the square root of the right side: 3.113590282 Break this problem into two subproblems by setting (x + -2.166666667) equal to 3.113590282 and -3.113590282.Subproblem 1
x + -2.166666667 = 3.113590282 Simplifying x + -2.166666667 = 3.113590282 Reorder the terms: -2.166666667 + x = 3.113590282 Solving -2.166666667 + x = 3.113590282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = 3.113590282 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 3.113590282 + 2.166666667 x = 3.113590282 + 2.166666667 Combine like terms: 3.113590282 + 2.166666667 = 5.280256949 x = 5.280256949 Simplifying x = 5.280256949Subproblem 2
x + -2.166666667 = -3.113590282 Simplifying x + -2.166666667 = -3.113590282 Reorder the terms: -2.166666667 + x = -3.113590282 Solving -2.166666667 + x = -3.113590282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = -3.113590282 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -3.113590282 + 2.166666667 x = -3.113590282 + 2.166666667 Combine like terms: -3.113590282 + 2.166666667 = -0.946923615 x = -0.946923615 Simplifying x = -0.946923615Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.280256949, -0.946923615}
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