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Simplifying 30x2 + 30x = 500 Reorder the terms: 30x + 30x2 = 500 Solving 30x + 30x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + 30x + 30x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 30x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-50 + 3x + 3x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-50 + 3x + 3x2)' equal to zero and attempt to solve: Simplifying -50 + 3x + 3x2 = 0 Solving -50 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.66666667 + x + x2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + x + 16.66666667 + x2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + x + x2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + x + x2 = 0 + 16.66666667 x + x2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 x + x2 = 16.66666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 16.66666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 16.66666667 + 0.25 Combine like terms: 16.66666667 + 0.25 = 16.91666667 1.25 + x2 = 16.91666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 16.91666667 Calculate the square root of the right side: 4.11298756 Break this problem into two subproblems by setting (x + 0.5) equal to 4.11298756 and -4.11298756.Subproblem 1
x + 0.5 = 4.11298756 Simplifying x + 0.5 = 4.11298756 Reorder the terms: 0.5 + x = 4.11298756 Solving 0.5 + x = 4.11298756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.11298756 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.11298756 + -0.5 x = 4.11298756 + -0.5 Combine like terms: 4.11298756 + -0.5 = 3.61298756 x = 3.61298756 Simplifying x = 3.61298756Subproblem 2
x + 0.5 = -4.11298756 Simplifying x + 0.5 = -4.11298756 Reorder the terms: 0.5 + x = -4.11298756 Solving 0.5 + x = -4.11298756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.11298756 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.11298756 + -0.5 x = -4.11298756 + -0.5 Combine like terms: -4.11298756 + -0.5 = -4.61298756 x = -4.61298756 Simplifying x = -4.61298756Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.61298756, -4.61298756}Solution
x = {3.61298756, -4.61298756}
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