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Simplifying 3x(2x + -5) = 2(x + -4) Reorder the terms: 3x(-5 + 2x) = 2(x + -4) (-5 * 3x + 2x * 3x) = 2(x + -4) (-15x + 6x2) = 2(x + -4) Reorder the terms: -15x + 6x2 = 2(-4 + x) -15x + 6x2 = (-4 * 2 + x * 2) -15x + 6x2 = (-8 + 2x) Solving -15x + 6x2 = -8 + 2x Solving for variable 'x'. Reorder the terms: 8 + -15x + -2x + 6x2 = -8 + 2x + 8 + -2x Combine like terms: -15x + -2x = -17x 8 + -17x + 6x2 = -8 + 2x + 8 + -2x Reorder the terms: 8 + -17x + 6x2 = -8 + 8 + 2x + -2x Combine like terms: -8 + 8 = 0 8 + -17x + 6x2 = 0 + 2x + -2x 8 + -17x + 6x2 = 2x + -2x Combine like terms: 2x + -2x = 0 8 + -17x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.333333333 + -2.833333333x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -2.833333333x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -2.833333333x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -2.833333333x + x2 = 0 + -1.333333333 -2.833333333x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -2.833333333x + x2 = -1.333333333 The x term is -2.833333333x. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333x + 2.006944445 + x2 = -1.333333333 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333x + x2 = -1.333333333 + 2.006944445 Combine like terms: -1.333333333 + 2.006944445 = 0.673611112 2.006944445 + -2.833333333x + x2 = 0.673611112 Factor a perfect square on the left side: (x + -1.416666667)(x + -1.416666667) = 0.673611112 Calculate the square root of the right side: 0.820738151 Break this problem into two subproblems by setting (x + -1.416666667) equal to 0.820738151 and -0.820738151.Subproblem 1
x + -1.416666667 = 0.820738151 Simplifying x + -1.416666667 = 0.820738151 Reorder the terms: -1.416666667 + x = 0.820738151 Solving -1.416666667 + x = 0.820738151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = 0.820738151 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = 0.820738151 + 1.416666667 x = 0.820738151 + 1.416666667 Combine like terms: 0.820738151 + 1.416666667 = 2.237404818 x = 2.237404818 Simplifying x = 2.237404818Subproblem 2
x + -1.416666667 = -0.820738151 Simplifying x + -1.416666667 = -0.820738151 Reorder the terms: -1.416666667 + x = -0.820738151 Solving -1.416666667 + x = -0.820738151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = -0.820738151 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = -0.820738151 + 1.416666667 x = -0.820738151 + 1.416666667 Combine like terms: -0.820738151 + 1.416666667 = 0.595928516 x = 0.595928516 Simplifying x = 0.595928516Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.237404818, 0.595928516}
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