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Simplifying 100x + 100x2 + -30 = 0 Reorder the terms: -30 + 100x + 100x2 = 0 Solving -30 + 100x + 100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-3 + 10x + 10x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-3 + 10x + 10x2)' equal to zero and attempt to solve: Simplifying -3 + 10x + 10x2 = 0 Solving -3 + 10x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x + x2 = 0.0 + 0.3 x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 x + x2 = 0.3 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 = 0.3 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.3 + 0.25 Combine like terms: 0.3 + 0.25 = 0.55 1.25 + x2 = 0.55 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.55 Calculate the square root of the right side: 0.741619849 Break this problem into two subproblems by setting (x + 0.5) equal to 0.741619849 and -0.741619849.Subproblem 1
x + 0.5 = 0.741619849 Simplifying x + 0.5 = 0.741619849 Reorder the terms: 0.5 + x = 0.741619849 Solving 0.5 + x = 0.741619849 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 = 0.741619849 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.741619849 + -0.5 x = 0.741619849 + -0.5 Combine like terms: 0.741619849 + -0.5 = 0.241619849 x = 0.241619849 Simplifying x = 0.241619849Subproblem 2
x + 0.5 = -0.741619849 Simplifying x + 0.5 = -0.741619849 Reorder the terms: 0.5 + x = -0.741619849 Solving 0.5 + x = -0.741619849 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 = -0.741619849 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.741619849 + -0.5 x = -0.741619849 + -0.5 Combine like terms: -0.741619849 + -0.5 = -1.241619849 x = -1.241619849 Simplifying x = -1.241619849Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.241619849, -1.241619849}Solution
x = {0.241619849, -1.241619849}
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