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Simplifying 3(x + -5)(2x + 1) = 3 + -1x Reorder the terms: 3(-5 + x)(2x + 1) = 3 + -1x Reorder the terms: 3(-5 + x)(1 + 2x) = 3 + -1x Multiply (-5 + x) * (1 + 2x) 3(-5(1 + 2x) + x(1 + 2x)) = 3 + -1x 3((1 * -5 + 2x * -5) + x(1 + 2x)) = 3 + -1x 3((-5 + -10x) + x(1 + 2x)) = 3 + -1x 3(-5 + -10x + (1 * x + 2x * x)) = 3 + -1x 3(-5 + -10x + (1x + 2x2)) = 3 + -1x Combine like terms: -10x + 1x = -9x 3(-5 + -9x + 2x2) = 3 + -1x (-5 * 3 + -9x * 3 + 2x2 * 3) = 3 + -1x (-15 + -27x + 6x2) = 3 + -1x Solving -15 + -27x + 6x2 = 3 + -1x Solving for variable 'x'. Reorder the terms: -15 + -3 + -27x + x + 6x2 = 3 + -1x + -3 + x Combine like terms: -15 + -3 = -18 -18 + -27x + x + 6x2 = 3 + -1x + -3 + x Combine like terms: -27x + x = -26x -18 + -26x + 6x2 = 3 + -1x + -3 + x Reorder the terms: -18 + -26x + 6x2 = 3 + -3 + -1x + x Combine like terms: 3 + -3 = 0 -18 + -26x + 6x2 = 0 + -1x + x -18 + -26x + 6x2 = -1x + x Combine like terms: -1x + x = 0 -18 + -26x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -13x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -13x + 3x2)' equal to zero and attempt to solve: Simplifying -9 + -13x + 3x2 = 0 Solving -9 + -13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + -4.333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -4.333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -4.333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4.333333333x + x2 = 0 + 3 -4.333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4.333333333x + x2 = 3 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 = 3 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333x + x2 = 3 + 4.694444446 Combine like terms: 3 + 4.694444446 = 7.694444446 4.694444446 + -4.333333333x + x2 = 7.694444446 Factor a perfect square on the left side: (x + -2.166666667)(x + -2.166666667) = 7.694444446 Calculate the square root of the right side: 2.773886163 Break this problem into two subproblems by setting (x + -2.166666667) equal to 2.773886163 and -2.773886163.Subproblem 1
x + -2.166666667 = 2.773886163 Simplifying x + -2.166666667 = 2.773886163 Reorder the terms: -2.166666667 + x = 2.773886163 Solving -2.166666667 + x = 2.773886163 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 = 2.773886163 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 2.773886163 + 2.166666667 x = 2.773886163 + 2.166666667 Combine like terms: 2.773886163 + 2.166666667 = 4.94055283 x = 4.94055283 Simplifying x = 4.94055283Subproblem 2
x + -2.166666667 = -2.773886163 Simplifying x + -2.166666667 = -2.773886163 Reorder the terms: -2.166666667 + x = -2.773886163 Solving -2.166666667 + x = -2.773886163 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 = -2.773886163 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -2.773886163 + 2.166666667 x = -2.773886163 + 2.166666667 Combine like terms: -2.773886163 + 2.166666667 = -0.607219496 x = -0.607219496 Simplifying x = -0.607219496Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.94055283, -0.607219496}Solution
x = {4.94055283, -0.607219496}
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