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Simplifying 10x2 + -6x + -18000 = 0 Reorder the terms: -18000 + -6x + 10x2 = 0 Solving -18000 + -6x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9000 + -3x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9000 + -3x + 5x2)' equal to zero and attempt to solve: Simplifying -9000 + -3x + 5x2 = 0 Solving -9000 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1800 + -0.6x + x2 = 0 Move the constant term to the right: Add '1800' to each side of the equation. -1800 + -0.6x + 1800 + x2 = 0 + 1800 Reorder the terms: -1800 + 1800 + -0.6x + x2 = 0 + 1800 Combine like terms: -1800 + 1800 = 0 0 + -0.6x + x2 = 0 + 1800 -0.6x + x2 = 0 + 1800 Combine like terms: 0 + 1800 = 1800 -0.6x + x2 = 1800 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 = 1800 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 1800 + 0.09 Combine like terms: 1800 + 0.09 = 1800.09 0.09 + -0.6x + x2 = 1800.09 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 1800.09 Calculate the square root of the right side: 42.427467518 Break this problem into two subproblems by setting (x + -0.3) equal to 42.427467518 and -42.427467518.Subproblem 1
x + -0.3 = 42.427467518 Simplifying x + -0.3 = 42.427467518 Reorder the terms: -0.3 + x = 42.427467518 Solving -0.3 + x = 42.427467518 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 = 42.427467518 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 42.427467518 + 0.3 x = 42.427467518 + 0.3 Combine like terms: 42.427467518 + 0.3 = 42.727467518 x = 42.727467518 Simplifying x = 42.727467518Subproblem 2
x + -0.3 = -42.427467518 Simplifying x + -0.3 = -42.427467518 Reorder the terms: -0.3 + x = -42.427467518 Solving -0.3 + x = -42.427467518 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 = -42.427467518 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -42.427467518 + 0.3 x = -42.427467518 + 0.3 Combine like terms: -42.427467518 + 0.3 = -42.127467518 x = -42.127467518 Simplifying x = -42.127467518Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.727467518, -42.127467518}Solution
x = {42.727467518, -42.127467518}
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