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Simplifying 0.3x(x + 100) = 500 Reorder the terms: 0.3x(100 + x) = 500 (100 * 0.3x + x * 0.3x) = 500 (30x + 0.3x2) = 500 Solving 30x + 0.3x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + 30x + 0.3x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 30x + 0.3x2 = 0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -1666.666667 + 100x + x2 = 0 Move the constant term to the right: Add '1666.666667' to each side of the equation. -1666.666667 + 100x + 1666.666667 + x2 = 0 + 1666.666667 Reorder the terms: -1666.666667 + 1666.666667 + 100x + x2 = 0 + 1666.666667 Combine like terms: -1666.666667 + 1666.666667 = 0.000000 0.000000 + 100x + x2 = 0 + 1666.666667 100x + x2 = 0 + 1666.666667 Combine like terms: 0 + 1666.666667 = 1666.666667 100x + x2 = 1666.666667 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 1666.666667 + 2500 Reorder the terms: 2500 + 100x + x2 = 1666.666667 + 2500 Combine like terms: 1666.666667 + 2500 = 4166.666667 2500 + 100x + x2 = 4166.666667 Factor a perfect square on the left side: (x + 50)(x + 50) = 4166.666667 Calculate the square root of the right side: 64.549722439 Break this problem into two subproblems by setting (x + 50) equal to 64.549722439 and -64.549722439.Subproblem 1
x + 50 = 64.549722439 Simplifying x + 50 = 64.549722439 Reorder the terms: 50 + x = 64.549722439 Solving 50 + x = 64.549722439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 64.549722439 + -50 Combine like terms: 50 + -50 = 0 0 + x = 64.549722439 + -50 x = 64.549722439 + -50 Combine like terms: 64.549722439 + -50 = 14.549722439 x = 14.549722439 Simplifying x = 14.549722439Subproblem 2
x + 50 = -64.549722439 Simplifying x + 50 = -64.549722439 Reorder the terms: 50 + x = -64.549722439 Solving 50 + x = -64.549722439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -64.549722439 + -50 Combine like terms: 50 + -50 = 0 0 + x = -64.549722439 + -50 x = -64.549722439 + -50 Combine like terms: -64.549722439 + -50 = -114.549722439 x = -114.549722439 Simplifying x = -114.549722439Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.549722439, -114.549722439}
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