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Simplifying 4x2 + -116x + 159 = 0 Reorder the terms: 159 + -116x + 4x2 = 0 Solving 159 + -116x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 39.75 + -29x + x2 = 0 Move the constant term to the right: Add '-39.75' to each side of the equation. 39.75 + -29x + -39.75 + x2 = 0 + -39.75 Reorder the terms: 39.75 + -39.75 + -29x + x2 = 0 + -39.75 Combine like terms: 39.75 + -39.75 = 0.00 0.00 + -29x + x2 = 0 + -39.75 -29x + x2 = 0 + -39.75 Combine like terms: 0 + -39.75 = -39.75 -29x + x2 = -39.75 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -39.75 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -39.75 + 210.25 Combine like terms: -39.75 + 210.25 = 170.5 210.25 + -29x + x2 = 170.5 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 170.5 Calculate the square root of the right side: 13.057564857 Break this problem into two subproblems by setting (x + -14.5) equal to 13.057564857 and -13.057564857.Subproblem 1
x + -14.5 = 13.057564857 Simplifying x + -14.5 = 13.057564857 Reorder the terms: -14.5 + x = 13.057564857 Solving -14.5 + x = 13.057564857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 13.057564857 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 13.057564857 + 14.5 x = 13.057564857 + 14.5 Combine like terms: 13.057564857 + 14.5 = 27.557564857 x = 27.557564857 Simplifying x = 27.557564857Subproblem 2
x + -14.5 = -13.057564857 Simplifying x + -14.5 = -13.057564857 Reorder the terms: -14.5 + x = -13.057564857 Solving -14.5 + x = -13.057564857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -13.057564857 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -13.057564857 + 14.5 x = -13.057564857 + 14.5 Combine like terms: -13.057564857 + 14.5 = 1.442435143 x = 1.442435143 Simplifying x = 1.442435143Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.557564857, 1.442435143}
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