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Simplifying -0.06x2 + 115x + -175 = 0 Reorder the terms: -175 + 115x + -0.06x2 = 0 Solving -175 + 115x + -0.06x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.06 the coefficient of the squared term: Divide each side by '-0.06'. 2916.666667 + -1916.666667x + x2 = 0 Move the constant term to the right: Add '-2916.666667' to each side of the equation. 2916.666667 + -1916.666667x + -2916.666667 + x2 = 0 + -2916.666667 Reorder the terms: 2916.666667 + -2916.666667 + -1916.666667x + x2 = 0 + -2916.666667 Combine like terms: 2916.666667 + -2916.666667 = 0.000000 0.000000 + -1916.666667x + x2 = 0 + -2916.666667 -1916.666667x + x2 = 0 + -2916.666667 Combine like terms: 0 + -2916.666667 = -2916.666667 -1916.666667x + x2 = -2916.666667 The x term is -1916.666667x. Take half its coefficient (-958.3333335). Square it (918402.7781) and add it to both sides. Add '918402.7781' to each side of the equation. -1916.666667x + 918402.7781 + x2 = -2916.666667 + 918402.7781 Reorder the terms: 918402.7781 + -1916.666667x + x2 = -2916.666667 + 918402.7781 Combine like terms: -2916.666667 + 918402.7781 = 915486.111433 918402.7781 + -1916.666667x + x2 = 915486.111433 Factor a perfect square on the left side: (x + -958.3333335)(x + -958.3333335) = 915486.111433 Calculate the square root of the right side: 956.810384263 Break this problem into two subproblems by setting (x + -958.3333335) equal to 956.810384263 and -956.810384263.Subproblem 1
x + -958.3333335 = 956.810384263 Simplifying x + -958.3333335 = 956.810384263 Reorder the terms: -958.3333335 + x = 956.810384263 Solving -958.3333335 + x = 956.810384263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '958.3333335' to each side of the equation. -958.3333335 + 958.3333335 + x = 956.810384263 + 958.3333335 Combine like terms: -958.3333335 + 958.3333335 = 0.0000000 0.0000000 + x = 956.810384263 + 958.3333335 x = 956.810384263 + 958.3333335 Combine like terms: 956.810384263 + 958.3333335 = 1915.143717763 x = 1915.143717763 Simplifying x = 1915.143717763Subproblem 2
x + -958.3333335 = -956.810384263 Simplifying x + -958.3333335 = -956.810384263 Reorder the terms: -958.3333335 + x = -956.810384263 Solving -958.3333335 + x = -956.810384263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '958.3333335' to each side of the equation. -958.3333335 + 958.3333335 + x = -956.810384263 + 958.3333335 Combine like terms: -958.3333335 + 958.3333335 = 0.0000000 0.0000000 + x = -956.810384263 + 958.3333335 x = -956.810384263 + 958.3333335 Combine like terms: -956.810384263 + 958.3333335 = 1.522949237 x = 1.522949237 Simplifying x = 1.522949237Solution
The solution to the problem is based on the solutions from the subproblems. x = {1915.143717763, 1.522949237}
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