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Simplifying -1x2 + 35x + -47 = 0 Reorder the terms: -47 + 35x + -1x2 = 0 Solving -47 + 35x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 47 + -35x + x2 = 0 Move the constant term to the right: Add '-47' to each side of the equation. 47 + -35x + -47 + x2 = 0 + -47 Reorder the terms: 47 + -47 + -35x + x2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -35x + x2 = 0 + -47 -35x + x2 = 0 + -47 Combine like terms: 0 + -47 = -47 -35x + x2 = -47 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = -47 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -47 + 306.25 Combine like terms: -47 + 306.25 = 259.25 306.25 + -35x + x2 = 259.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 259.25 Calculate the square root of the right side: 16.101242188 Break this problem into two subproblems by setting (x + -17.5) equal to 16.101242188 and -16.101242188.Subproblem 1
x + -17.5 = 16.101242188 Simplifying x + -17.5 = 16.101242188 Reorder the terms: -17.5 + x = 16.101242188 Solving -17.5 + x = 16.101242188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 16.101242188 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 16.101242188 + 17.5 x = 16.101242188 + 17.5 Combine like terms: 16.101242188 + 17.5 = 33.601242188 x = 33.601242188 Simplifying x = 33.601242188Subproblem 2
x + -17.5 = -16.101242188 Simplifying x + -17.5 = -16.101242188 Reorder the terms: -17.5 + x = -16.101242188 Solving -17.5 + x = -16.101242188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -16.101242188 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -16.101242188 + 17.5 x = -16.101242188 + 17.5 Combine like terms: -16.101242188 + 17.5 = 1.398757812 x = 1.398757812 Simplifying x = 1.398757812Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.601242188, 1.398757812}
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