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Simplifying 6x + 3x2 = 500 Solving 6x + 3x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + 6x + 3x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -166.6666667 + 2x + x2 = 0 Move the constant term to the right: Add '166.6666667' to each side of the equation. -166.6666667 + 2x + 166.6666667 + x2 = 0 + 166.6666667 Reorder the terms: -166.6666667 + 166.6666667 + 2x + x2 = 0 + 166.6666667 Combine like terms: -166.6666667 + 166.6666667 = 0.0000000 0.0000000 + 2x + x2 = 0 + 166.6666667 2x + x2 = 0 + 166.6666667 Combine like terms: 0 + 166.6666667 = 166.6666667 2x + x2 = 166.6666667 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 166.6666667 + 1 Reorder the terms: 1 + 2x + x2 = 166.6666667 + 1 Combine like terms: 166.6666667 + 1 = 167.6666667 1 + 2x + x2 = 167.6666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 167.6666667 Calculate the square root of the right side: 12.948616401 Break this problem into two subproblems by setting (x + 1) equal to 12.948616401 and -12.948616401.Subproblem 1
x + 1 = 12.948616401 Simplifying x + 1 = 12.948616401 Reorder the terms: 1 + x = 12.948616401 Solving 1 + x = 12.948616401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 12.948616401 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.948616401 + -1 x = 12.948616401 + -1 Combine like terms: 12.948616401 + -1 = 11.948616401 x = 11.948616401 Simplifying x = 11.948616401Subproblem 2
x + 1 = -12.948616401 Simplifying x + 1 = -12.948616401 Reorder the terms: 1 + x = -12.948616401 Solving 1 + x = -12.948616401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -12.948616401 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.948616401 + -1 x = -12.948616401 + -1 Combine like terms: -12.948616401 + -1 = -13.948616401 x = -13.948616401 Simplifying x = -13.948616401Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.948616401, -13.948616401}
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