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Simplifying -73x2 + 4250x + -5040 = 0 Reorder the terms: -5040 + 4250x + -73x2 = 0 Solving -5040 + 4250x + -73x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -73 the coefficient of the squared term: Divide each side by '-73'. 69.04109589 + -58.21917808x + x2 = 0 Move the constant term to the right: Add '-69.04109589' to each side of the equation. 69.04109589 + -58.21917808x + -69.04109589 + x2 = 0 + -69.04109589 Reorder the terms: 69.04109589 + -69.04109589 + -58.21917808x + x2 = 0 + -69.04109589 Combine like terms: 69.04109589 + -69.04109589 = 0.00000000 0.00000000 + -58.21917808x + x2 = 0 + -69.04109589 -58.21917808x + x2 = 0 + -69.04109589 Combine like terms: 0 + -69.04109589 = -69.04109589 -58.21917808x + x2 = -69.04109589 The x term is -58.21917808x. Take half its coefficient (-29.10958904). Square it (847.3681741) and add it to both sides. Add '847.3681741' to each side of the equation. -58.21917808x + 847.3681741 + x2 = -69.04109589 + 847.3681741 Reorder the terms: 847.3681741 + -58.21917808x + x2 = -69.04109589 + 847.3681741 Combine like terms: -69.04109589 + 847.3681741 = 778.32707821 847.3681741 + -58.21917808x + x2 = 778.32707821 Factor a perfect square on the left side: (x + -29.10958904)(x + -29.10958904) = 778.32707821 Calculate the square root of the right side: 27.898513907 Break this problem into two subproblems by setting (x + -29.10958904) equal to 27.898513907 and -27.898513907.Subproblem 1
x + -29.10958904 = 27.898513907 Simplifying x + -29.10958904 = 27.898513907 Reorder the terms: -29.10958904 + x = 27.898513907 Solving -29.10958904 + x = 27.898513907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.10958904' to each side of the equation. -29.10958904 + 29.10958904 + x = 27.898513907 + 29.10958904 Combine like terms: -29.10958904 + 29.10958904 = 0.00000000 0.00000000 + x = 27.898513907 + 29.10958904 x = 27.898513907 + 29.10958904 Combine like terms: 27.898513907 + 29.10958904 = 57.008102947 x = 57.008102947 Simplifying x = 57.008102947Subproblem 2
x + -29.10958904 = -27.898513907 Simplifying x + -29.10958904 = -27.898513907 Reorder the terms: -29.10958904 + x = -27.898513907 Solving -29.10958904 + x = -27.898513907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.10958904' to each side of the equation. -29.10958904 + 29.10958904 + x = -27.898513907 + 29.10958904 Combine like terms: -29.10958904 + 29.10958904 = 0.00000000 0.00000000 + x = -27.898513907 + 29.10958904 x = -27.898513907 + 29.10958904 Combine like terms: -27.898513907 + 29.10958904 = 1.211075133 x = 1.211075133 Simplifying x = 1.211075133Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.008102947, 1.211075133}
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