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Simplifying 0.1x2 + -5x = 14 Reorder the terms: -5x + 0.1x2 = 14 Solving -5x + 0.1x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + -5x + 0.1x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -5x + 0.1x2 = 0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -140 + -50x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + -50x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + -50x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -50x + x2 = 0 + 140 -50x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 -50x + x2 = 140 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 140 + 625 Reorder the terms: 625 + -50x + x2 = 140 + 625 Combine like terms: 140 + 625 = 765 625 + -50x + x2 = 765 Factor a perfect square on the left side: (x + -25)(x + -25) = 765 Calculate the square root of the right side: 27.658633372 Break this problem into two subproblems by setting (x + -25) equal to 27.658633372 and -27.658633372.Subproblem 1
x + -25 = 27.658633372 Simplifying x + -25 = 27.658633372 Reorder the terms: -25 + x = 27.658633372 Solving -25 + x = 27.658633372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 27.658633372 + 25 Combine like terms: -25 + 25 = 0 0 + x = 27.658633372 + 25 x = 27.658633372 + 25 Combine like terms: 27.658633372 + 25 = 52.658633372 x = 52.658633372 Simplifying x = 52.658633372Subproblem 2
x + -25 = -27.658633372 Simplifying x + -25 = -27.658633372 Reorder the terms: -25 + x = -27.658633372 Solving -25 + x = -27.658633372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -27.658633372 + 25 Combine like terms: -25 + 25 = 0 0 + x = -27.658633372 + 25 x = -27.658633372 + 25 Combine like terms: -27.658633372 + 25 = -2.658633372 x = -2.658633372 Simplifying x = -2.658633372Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.658633372, -2.658633372}
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