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Simplifying 3x(5 + -2x) = x + -21 (5 * 3x + -2x * 3x) = x + -21 (15x + -6x2) = x + -21 Reorder the terms: 15x + -6x2 = -21 + x Solving 15x + -6x2 = -21 + x Solving for variable 'x'. Reorder the terms: 21 + 15x + -1x + -6x2 = -21 + x + 21 + -1x Combine like terms: 15x + -1x = 14x 21 + 14x + -6x2 = -21 + x + 21 + -1x Reorder the terms: 21 + 14x + -6x2 = -21 + 21 + x + -1x Combine like terms: -21 + 21 = 0 21 + 14x + -6x2 = 0 + x + -1x 21 + 14x + -6x2 = x + -1x Combine like terms: x + -1x = 0 21 + 14x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -3.5 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -2.333333333x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -2.333333333x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -2.333333333x + x2 = 0 + 3.5 -2.333333333x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -2.333333333x + x2 = 3.5 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 3.5 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 3.5 + 1.361111112 Combine like terms: 3.5 + 1.361111112 = 4.861111112 1.361111112 + -2.333333333x + x2 = 4.861111112 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 4.861111112 Calculate the square root of the right side: 2.204792759 Break this problem into two subproblems by setting (x + -1.166666667) equal to 2.204792759 and -2.204792759.Subproblem 1
x + -1.166666667 = 2.204792759 Simplifying x + -1.166666667 = 2.204792759 Reorder the terms: -1.166666667 + x = 2.204792759 Solving -1.166666667 + x = 2.204792759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 2.204792759 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 2.204792759 + 1.166666667 x = 2.204792759 + 1.166666667 Combine like terms: 2.204792759 + 1.166666667 = 3.371459426 x = 3.371459426 Simplifying x = 3.371459426Subproblem 2
x + -1.166666667 = -2.204792759 Simplifying x + -1.166666667 = -2.204792759 Reorder the terms: -1.166666667 + x = -2.204792759 Solving -1.166666667 + x = -2.204792759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -2.204792759 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -2.204792759 + 1.166666667 x = -2.204792759 + 1.166666667 Combine like terms: -2.204792759 + 1.166666667 = -1.038126092 x = -1.038126092 Simplifying x = -1.038126092Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.371459426, -1.038126092}
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