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Simplifying 3x2 + 7x = 500 Reorder the terms: 7x + 3x2 = 500 Solving 7x + 3x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + 7x + 3x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -166.6666667 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '166.6666667' to each side of the equation. -166.6666667 + 2.333333333x + 166.6666667 + x2 = 0 + 166.6666667 Reorder the terms: -166.6666667 + 166.6666667 + 2.333333333x + x2 = 0 + 166.6666667 Combine like terms: -166.6666667 + 166.6666667 = 0.0000000 0.0000000 + 2.333333333x + x2 = 0 + 166.6666667 2.333333333x + x2 = 0 + 166.6666667 Combine like terms: 0 + 166.6666667 = 166.6666667 2.333333333x + x2 = 166.6666667 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 = 166.6666667 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 166.6666667 + 1.361111112 Combine like terms: 166.6666667 + 1.361111112 = 168.027777812 1.361111112 + 2.333333333x + x2 = 168.027777812 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 168.027777812 Calculate the square root of the right side: 12.962552905 Break this problem into two subproblems by setting (x + 1.166666667) equal to 12.962552905 and -12.962552905.Subproblem 1
x + 1.166666667 = 12.962552905 Simplifying x + 1.166666667 = 12.962552905 Reorder the terms: 1.166666667 + x = 12.962552905 Solving 1.166666667 + x = 12.962552905 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 = 12.962552905 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 12.962552905 + -1.166666667 x = 12.962552905 + -1.166666667 Combine like terms: 12.962552905 + -1.166666667 = 11.795886238 x = 11.795886238 Simplifying x = 11.795886238Subproblem 2
x + 1.166666667 = -12.962552905 Simplifying x + 1.166666667 = -12.962552905 Reorder the terms: 1.166666667 + x = -12.962552905 Solving 1.166666667 + x = -12.962552905 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 = -12.962552905 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -12.962552905 + -1.166666667 x = -12.962552905 + -1.166666667 Combine like terms: -12.962552905 + -1.166666667 = -14.129219572 x = -14.129219572 Simplifying x = -14.129219572Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.795886238, -14.129219572}
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