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Simplifying 5x2 + -87x + 35 = 0 Reorder the terms: 35 + -87x + 5x2 = 0 Solving 35 + -87x + 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'. 7 + -17.4x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -17.4x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -17.4x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -17.4x + x2 = 0 + -7 -17.4x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -17.4x + x2 = -7 The x term is -17.4x. Take half its coefficient (-8.7). Square it (75.69) and add it to both sides. Add '75.69' to each side of the equation. -17.4x + 75.69 + x2 = -7 + 75.69 Reorder the terms: 75.69 + -17.4x + x2 = -7 + 75.69 Combine like terms: -7 + 75.69 = 68.69 75.69 + -17.4x + x2 = 68.69 Factor a perfect square on the left side: (x + -8.7)(x + -8.7) = 68.69 Calculate the square root of the right side: 8.28794305 Break this problem into two subproblems by setting (x + -8.7) equal to 8.28794305 and -8.28794305.Subproblem 1
x + -8.7 = 8.28794305 Simplifying x + -8.7 = 8.28794305 Reorder the terms: -8.7 + x = 8.28794305 Solving -8.7 + x = 8.28794305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.7' to each side of the equation. -8.7 + 8.7 + x = 8.28794305 + 8.7 Combine like terms: -8.7 + 8.7 = 0.0 0.0 + x = 8.28794305 + 8.7 x = 8.28794305 + 8.7 Combine like terms: 8.28794305 + 8.7 = 16.98794305 x = 16.98794305 Simplifying x = 16.98794305Subproblem 2
x + -8.7 = -8.28794305 Simplifying x + -8.7 = -8.28794305 Reorder the terms: -8.7 + x = -8.28794305 Solving -8.7 + x = -8.28794305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.7' to each side of the equation. -8.7 + 8.7 + x = -8.28794305 + 8.7 Combine like terms: -8.7 + 8.7 = 0.0 0.0 + x = -8.28794305 + 8.7 x = -8.28794305 + 8.7 Combine like terms: -8.28794305 + 8.7 = 0.41205695 x = 0.41205695 Simplifying x = 0.41205695Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.98794305, 0.41205695}
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