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Simplifying 0 = -1x2 + 35x + -190 Reorder the terms: 0 = -190 + 35x + -1x2 Solving 0 = -190 + 35x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 190 = 190 190 + -35x + x2 = -190 + 35x + -1x2 + 190 + -35x + x2 Reorder the terms: 190 + -35x + x2 = -190 + 190 + 35x + -35x + -1x2 + x2 Combine like terms: -190 + 190 = 0 190 + -35x + x2 = 0 + 35x + -35x + -1x2 + x2 190 + -35x + x2 = 35x + -35x + -1x2 + x2 Combine like terms: 35x + -35x = 0 190 + -35x + x2 = 0 + -1x2 + x2 190 + -35x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 190 + -35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-190' to each side of the equation. 190 + -35x + -190 + x2 = 0 + -190 Reorder the terms: 190 + -190 + -35x + x2 = 0 + -190 Combine like terms: 190 + -190 = 0 0 + -35x + x2 = 0 + -190 -35x + x2 = 0 + -190 Combine like terms: 0 + -190 = -190 -35x + x2 = -190 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 = -190 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -190 + 306.25 Combine like terms: -190 + 306.25 = 116.25 306.25 + -35x + x2 = 116.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 116.25 Calculate the square root of the right side: 10.781929326 Break this problem into two subproblems by setting (x + -17.5) equal to 10.781929326 and -10.781929326.Subproblem 1
x + -17.5 = 10.781929326 Simplifying x + -17.5 = 10.781929326 Reorder the terms: -17.5 + x = 10.781929326 Solving -17.5 + x = 10.781929326 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 = 10.781929326 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 10.781929326 + 17.5 x = 10.781929326 + 17.5 Combine like terms: 10.781929326 + 17.5 = 28.281929326 x = 28.281929326 Simplifying x = 28.281929326Subproblem 2
x + -17.5 = -10.781929326 Simplifying x + -17.5 = -10.781929326 Reorder the terms: -17.5 + x = -10.781929326 Solving -17.5 + x = -10.781929326 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 = -10.781929326 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -10.781929326 + 17.5 x = -10.781929326 + 17.5 Combine like terms: -10.781929326 + 17.5 = 6.718070674 x = 6.718070674 Simplifying x = 6.718070674Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.281929326, 6.718070674}
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