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Simplifying 0 = -0.16x2 + 4x + 10 Reorder the terms: 0 = 10 + 4x + -0.16x2 Solving 0 = 10 + 4x + -0.16x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -4x + 0.16x2 = 10 + 4x + -0.16x2 + -10 + -4x + 0.16x2 Reorder the terms: -10 + -4x + 0.16x2 = 10 + -10 + 4x + -4x + -0.16x2 + 0.16x2 Combine like terms: 10 + -10 = 0 -10 + -4x + 0.16x2 = 0 + 4x + -4x + -0.16x2 + 0.16x2 -10 + -4x + 0.16x2 = 4x + -4x + -0.16x2 + 0.16x2 Combine like terms: 4x + -4x = 0 -10 + -4x + 0.16x2 = 0 + -0.16x2 + 0.16x2 -10 + -4x + 0.16x2 = -0.16x2 + 0.16x2 Combine like terms: -0.16x2 + 0.16x2 = 0.00 -10 + -4x + 0.16x2 = 0.00 Begin completing the square. Divide all terms by 0.16 the coefficient of the squared term: Divide each side by '0.16'. -62.5 + -25x + x2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + -25x + 62.5 + x2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + -25x + x2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + -25x + x2 = 0 + 62.5 -25x + x2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 -25x + x2 = 62.5 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = 62.5 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 62.5 + 156.25 Combine like terms: 62.5 + 156.25 = 218.75 156.25 + -25x + x2 = 218.75 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 218.75 Calculate the square root of the right side: 14.790199458 Break this problem into two subproblems by setting (x + -12.5) equal to 14.790199458 and -14.790199458.Subproblem 1
x + -12.5 = 14.790199458 Simplifying x + -12.5 = 14.790199458 Reorder the terms: -12.5 + x = 14.790199458 Solving -12.5 + x = 14.790199458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 14.790199458 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 14.790199458 + 12.5 x = 14.790199458 + 12.5 Combine like terms: 14.790199458 + 12.5 = 27.290199458 x = 27.290199458 Simplifying x = 27.290199458Subproblem 2
x + -12.5 = -14.790199458 Simplifying x + -12.5 = -14.790199458 Reorder the terms: -12.5 + x = -14.790199458 Solving -12.5 + x = -14.790199458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -14.790199458 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -14.790199458 + 12.5 x = -14.790199458 + 12.5 Combine like terms: -14.790199458 + 12.5 = -2.290199458 x = -2.290199458 Simplifying x = -2.290199458Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.290199458, -2.290199458}
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