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Simplifying 120 = (3x + -7)(x) Reorder the terms: 120 = (-7 + 3x)(x) Reorder the terms for easier multiplication: 120 = x(-7 + 3x) 120 = (-7 * x + 3x * x) 120 = (-7x + 3x2) Solving 120 = -7x + 3x2 Solving for variable 'x'. Reorder the terms: 120 + 7x + -3x2 = -7x + 7x + 3x2 + -3x2 Combine like terms: -7x + 7x = 0 120 + 7x + -3x2 = 0 + 3x2 + -3x2 120 + 7x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 120 + 7x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -40 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -2.333333333x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -2.333333333x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -2.333333333x + x2 = 0 + 40 -2.333333333x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -2.333333333x + x2 = 40 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 = 40 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 40 + 1.361111112 Combine like terms: 40 + 1.361111112 = 41.361111112 1.361111112 + -2.333333333x + x2 = 41.361111112 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 41.361111112 Calculate the square root of the right side: 6.431260461 Break this problem into two subproblems by setting (x + -1.166666667) equal to 6.431260461 and -6.431260461.Subproblem 1
x + -1.166666667 = 6.431260461 Simplifying x + -1.166666667 = 6.431260461 Reorder the terms: -1.166666667 + x = 6.431260461 Solving -1.166666667 + x = 6.431260461 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 = 6.431260461 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 6.431260461 + 1.166666667 x = 6.431260461 + 1.166666667 Combine like terms: 6.431260461 + 1.166666667 = 7.597927128 x = 7.597927128 Simplifying x = 7.597927128Subproblem 2
x + -1.166666667 = -6.431260461 Simplifying x + -1.166666667 = -6.431260461 Reorder the terms: -1.166666667 + x = -6.431260461 Solving -1.166666667 + x = -6.431260461 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 = -6.431260461 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -6.431260461 + 1.166666667 x = -6.431260461 + 1.166666667 Combine like terms: -6.431260461 + 1.166666667 = -5.264593794 x = -5.264593794 Simplifying x = -5.264593794Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.597927128, -5.264593794}
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