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Simplifying 5x2 + -58x + -87 = 0 Reorder the terms: -87 + -58x + 5x2 = 0 Solving -87 + -58x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -17.4 + -11.6x + x2 = 0 Move the constant term to the right: Add '17.4' to each side of the equation. -17.4 + -11.6x + 17.4 + x2 = 0 + 17.4 Reorder the terms: -17.4 + 17.4 + -11.6x + x2 = 0 + 17.4 Combine like terms: -17.4 + 17.4 = 0.0 0.0 + -11.6x + x2 = 0 + 17.4 -11.6x + x2 = 0 + 17.4 Combine like terms: 0 + 17.4 = 17.4 -11.6x + x2 = 17.4 The x term is -11.6x. Take half its coefficient (-5.8). Square it (33.64) and add it to both sides. Add '33.64' to each side of the equation. -11.6x + 33.64 + x2 = 17.4 + 33.64 Reorder the terms: 33.64 + -11.6x + x2 = 17.4 + 33.64 Combine like terms: 17.4 + 33.64 = 51.04 33.64 + -11.6x + x2 = 51.04 Factor a perfect square on the left side: (x + -5.8)(x + -5.8) = 51.04 Calculate the square root of the right side: 7.14422844 Break this problem into two subproblems by setting (x + -5.8) equal to 7.14422844 and -7.14422844.Subproblem 1
x + -5.8 = 7.14422844 Simplifying x + -5.8 = 7.14422844 Reorder the terms: -5.8 + x = 7.14422844 Solving -5.8 + x = 7.14422844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.8' to each side of the equation. -5.8 + 5.8 + x = 7.14422844 + 5.8 Combine like terms: -5.8 + 5.8 = 0.0 0.0 + x = 7.14422844 + 5.8 x = 7.14422844 + 5.8 Combine like terms: 7.14422844 + 5.8 = 12.94422844 x = 12.94422844 Simplifying x = 12.94422844Subproblem 2
x + -5.8 = -7.14422844 Simplifying x + -5.8 = -7.14422844 Reorder the terms: -5.8 + x = -7.14422844 Solving -5.8 + x = -7.14422844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.8' to each side of the equation. -5.8 + 5.8 + x = -7.14422844 + 5.8 Combine like terms: -5.8 + 5.8 = 0.0 0.0 + x = -7.14422844 + 5.8 x = -7.14422844 + 5.8 Combine like terms: -7.14422844 + 5.8 = -1.34422844 x = -1.34422844 Simplifying x = -1.34422844Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.94422844, -1.34422844}
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