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Simplifying 10x2 + -6x + -1800 = 0 Reorder the terms: -1800 + -6x + 10x2 = 0 Solving -1800 + -6x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-900 + -3x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-900 + -3x + 5x2)' equal to zero and attempt to solve: Simplifying -900 + -3x + 5x2 = 0 Solving -900 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -180 + -0.6x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + -0.6x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -0.6x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -0.6x + x2 = 0 + 180 -0.6x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -0.6x + x2 = 180 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 180 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 180 + 0.09 Combine like terms: 180 + 0.09 = 180.09 0.09 + -0.6x + x2 = 180.09 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 180.09 Calculate the square root of the right side: 13.419761548 Break this problem into two subproblems by setting (x + -0.3) equal to 13.419761548 and -13.419761548.Subproblem 1
x + -0.3 = 13.419761548 Simplifying x + -0.3 = 13.419761548 Reorder the terms: -0.3 + x = 13.419761548 Solving -0.3 + x = 13.419761548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 13.419761548 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 13.419761548 + 0.3 x = 13.419761548 + 0.3 Combine like terms: 13.419761548 + 0.3 = 13.719761548 x = 13.719761548 Simplifying x = 13.719761548Subproblem 2
x + -0.3 = -13.419761548 Simplifying x + -0.3 = -13.419761548 Reorder the terms: -0.3 + x = -13.419761548 Solving -0.3 + x = -13.419761548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -13.419761548 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -13.419761548 + 0.3 x = -13.419761548 + 0.3 Combine like terms: -13.419761548 + 0.3 = -13.119761548 x = -13.119761548 Simplifying x = -13.119761548Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.719761548, -13.119761548}Solution
x = {13.719761548, -13.119761548}
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